// Copyright 2016 Emilie Gillet.
//
// Author: Emilie Gillet (emilie.o.gillet@gmail.com)
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
// 
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
// 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
// 
// See http://creativecommons.org/licenses/MIT/ for more information.
//
// -----------------------------------------------------------------------------
//
// Resources definitions.
//
// Automatically generated with:
// make resources


#include "plaits/resources.h"

namespace plaits {

const float lut_sine[] = {
   0.000000000e+00,  6.135884649e-03,  1.227153829e-02,  1.840672991e-02,
   2.454122852e-02,  3.067480318e-02,  3.680722294e-02,  4.293825693e-02,
   4.906767433e-02,  5.519524435e-02,  6.132073630e-02,  6.744391956e-02,
   7.356456360e-02,  7.968243797e-02,  8.579731234e-02,  9.190895650e-02,
   9.801714033e-02,  1.041216339e-01,  1.102222073e-01,  1.163186309e-01,
   1.224106752e-01,  1.284981108e-01,  1.345807085e-01,  1.406582393e-01,
   1.467304745e-01,  1.527971853e-01,  1.588581433e-01,  1.649131205e-01,
   1.709618888e-01,  1.770042204e-01,  1.830398880e-01,  1.890686641e-01,
   1.950903220e-01,  2.011046348e-01,  2.071113762e-01,  2.131103199e-01,
   2.191012402e-01,  2.250839114e-01,  2.310581083e-01,  2.370236060e-01,
   2.429801799e-01,  2.489276057e-01,  2.548656596e-01,  2.607941179e-01,
   2.667127575e-01,  2.726213554e-01,  2.785196894e-01,  2.844075372e-01,
   2.902846773e-01,  2.961508882e-01,  3.020059493e-01,  3.078496400e-01,
   3.136817404e-01,  3.195020308e-01,  3.253102922e-01,  3.311063058e-01,
   3.368898534e-01,  3.426607173e-01,  3.484186802e-01,  3.541635254e-01,
   3.598950365e-01,  3.656129978e-01,  3.713171940e-01,  3.770074102e-01,
   3.826834324e-01,  3.883450467e-01,  3.939920401e-01,  3.996241998e-01,
   4.052413140e-01,  4.108431711e-01,  4.164295601e-01,  4.220002708e-01,
   4.275550934e-01,  4.330938189e-01,  4.386162385e-01,  4.441221446e-01,
   4.496113297e-01,  4.550835871e-01,  4.605387110e-01,  4.659764958e-01,
   4.713967368e-01,  4.767992301e-01,  4.821837721e-01,  4.875501601e-01,
   4.928981922e-01,  4.982276670e-01,  5.035383837e-01,  5.088301425e-01,
   5.141027442e-01,  5.193559902e-01,  5.245896827e-01,  5.298036247e-01,
   5.349976199e-01,  5.401714727e-01,  5.453249884e-01,  5.504579729e-01,
   5.555702330e-01,  5.606615762e-01,  5.657318108e-01,  5.707807459e-01,
   5.758081914e-01,  5.808139581e-01,  5.857978575e-01,  5.907597019e-01,
   5.956993045e-01,  6.006164794e-01,  6.055110414e-01,  6.103828063e-01,
   6.152315906e-01,  6.200572118e-01,  6.248594881e-01,  6.296382389e-01,
   6.343932842e-01,  6.391244449e-01,  6.438315429e-01,  6.485144010e-01,
   6.531728430e-01,  6.578066933e-01,  6.624157776e-01,  6.669999223e-01,
   6.715589548e-01,  6.760927036e-01,  6.806009978e-01,  6.850836678e-01,
   6.895405447e-01,  6.939714609e-01,  6.983762494e-01,  7.027547445e-01,
   7.071067812e-01,  7.114321957e-01,  7.157308253e-01,  7.200025080e-01,
   7.242470830e-01,  7.284643904e-01,  7.326542717e-01,  7.368165689e-01,
   7.409511254e-01,  7.450577854e-01,  7.491363945e-01,  7.531867990e-01,
   7.572088465e-01,  7.612023855e-01,  7.651672656e-01,  7.691033376e-01,
   7.730104534e-01,  7.768884657e-01,  7.807372286e-01,  7.845565972e-01,
   7.883464276e-01,  7.921065773e-01,  7.958369046e-01,  7.995372691e-01,
   8.032075315e-01,  8.068475535e-01,  8.104571983e-01,  8.140363297e-01,
   8.175848132e-01,  8.211025150e-01,  8.245893028e-01,  8.280450453e-01,
   8.314696123e-01,  8.348628750e-01,  8.382247056e-01,  8.415549774e-01,
   8.448535652e-01,  8.481203448e-01,  8.513551931e-01,  8.545579884e-01,
   8.577286100e-01,  8.608669386e-01,  8.639728561e-01,  8.670462455e-01,
   8.700869911e-01,  8.730949784e-01,  8.760700942e-01,  8.790122264e-01,
   8.819212643e-01,  8.847970984e-01,  8.876396204e-01,  8.904487232e-01,
   8.932243012e-01,  8.959662498e-01,  8.986744657e-01,  9.013488470e-01,
   9.039892931e-01,  9.065957045e-01,  9.091679831e-01,  9.117060320e-01,
   9.142097557e-01,  9.166790599e-01,  9.191138517e-01,  9.215140393e-01,
   9.238795325e-01,  9.262102421e-01,  9.285060805e-01,  9.307669611e-01,
   9.329927988e-01,  9.351835099e-01,  9.373390119e-01,  9.394592236e-01,
   9.415440652e-01,  9.435934582e-01,  9.456073254e-01,  9.475855910e-01,
   9.495281806e-01,  9.514350210e-01,  9.533060404e-01,  9.551411683e-01,
   9.569403357e-01,  9.587034749e-01,  9.604305194e-01,  9.621214043e-01,
   9.637760658e-01,  9.653944417e-01,  9.669764710e-01,  9.685220943e-01,
   9.700312532e-01,  9.715038910e-01,  9.729399522e-01,  9.743393828e-01,
   9.757021300e-01,  9.770281427e-01,  9.783173707e-01,  9.795697657e-01,
   9.807852804e-01,  9.819638691e-01,  9.831054874e-01,  9.842100924e-01,
   9.852776424e-01,  9.863080972e-01,  9.873014182e-01,  9.882575677e-01,
   9.891765100e-01,  9.900582103e-01,  9.909026354e-01,  9.917097537e-01,
   9.924795346e-01,  9.932119492e-01,  9.939069700e-01,  9.945645707e-01,
   9.951847267e-01,  9.957674145e-01,  9.963126122e-01,  9.968202993e-01,
   9.972904567e-01,  9.977230666e-01,  9.981181129e-01,  9.984755806e-01,
   9.987954562e-01,  9.990777278e-01,  9.993223846e-01,  9.995294175e-01,
   9.996988187e-01,  9.998305818e-01,  9.999247018e-01,  9.999811753e-01,
   1.000000000e+00,  9.999811753e-01,  9.999247018e-01,  9.998305818e-01,
   9.996988187e-01,  9.995294175e-01,  9.993223846e-01,  9.990777278e-01,
   9.987954562e-01,  9.984755806e-01,  9.981181129e-01,  9.977230666e-01,
   9.972904567e-01,  9.968202993e-01,  9.963126122e-01,  9.957674145e-01,
   9.951847267e-01,  9.945645707e-01,  9.939069700e-01,  9.932119492e-01,
   9.924795346e-01,  9.917097537e-01,  9.909026354e-01,  9.900582103e-01,
   9.891765100e-01,  9.882575677e-01,  9.873014182e-01,  9.863080972e-01,
   9.852776424e-01,  9.842100924e-01,  9.831054874e-01,  9.819638691e-01,
   9.807852804e-01,  9.795697657e-01,  9.783173707e-01,  9.770281427e-01,
   9.757021300e-01,  9.743393828e-01,  9.729399522e-01,  9.715038910e-01,
   9.700312532e-01,  9.685220943e-01,  9.669764710e-01,  9.653944417e-01,
   9.637760658e-01,  9.621214043e-01,  9.604305194e-01,  9.587034749e-01,
   9.569403357e-01,  9.551411683e-01,  9.533060404e-01,  9.514350210e-01,
   9.495281806e-01,  9.475855910e-01,  9.456073254e-01,  9.435934582e-01,
   9.415440652e-01,  9.394592236e-01,  9.373390119e-01,  9.351835099e-01,
   9.329927988e-01,  9.307669611e-01,  9.285060805e-01,  9.262102421e-01,
   9.238795325e-01,  9.215140393e-01,  9.191138517e-01,  9.166790599e-01,
   9.142097557e-01,  9.117060320e-01,  9.091679831e-01,  9.065957045e-01,
   9.039892931e-01,  9.013488470e-01,  8.986744657e-01,  8.959662498e-01,
   8.932243012e-01,  8.904487232e-01,  8.876396204e-01,  8.847970984e-01,
   8.819212643e-01,  8.790122264e-01,  8.760700942e-01,  8.730949784e-01,
   8.700869911e-01,  8.670462455e-01,  8.639728561e-01,  8.608669386e-01,
   8.577286100e-01,  8.545579884e-01,  8.513551931e-01,  8.481203448e-01,
   8.448535652e-01,  8.415549774e-01,  8.382247056e-01,  8.348628750e-01,
   8.314696123e-01,  8.280450453e-01,  8.245893028e-01,  8.211025150e-01,
   8.175848132e-01,  8.140363297e-01,  8.104571983e-01,  8.068475535e-01,
   8.032075315e-01,  7.995372691e-01,  7.958369046e-01,  7.921065773e-01,
   7.883464276e-01,  7.845565972e-01,  7.807372286e-01,  7.768884657e-01,
   7.730104534e-01,  7.691033376e-01,  7.651672656e-01,  7.612023855e-01,
   7.572088465e-01,  7.531867990e-01,  7.491363945e-01,  7.450577854e-01,
   7.409511254e-01,  7.368165689e-01,  7.326542717e-01,  7.284643904e-01,
   7.242470830e-01,  7.200025080e-01,  7.157308253e-01,  7.114321957e-01,
   7.071067812e-01,  7.027547445e-01,  6.983762494e-01,  6.939714609e-01,
   6.895405447e-01,  6.850836678e-01,  6.806009978e-01,  6.760927036e-01,
   6.715589548e-01,  6.669999223e-01,  6.624157776e-01,  6.578066933e-01,
   6.531728430e-01,  6.485144010e-01,  6.438315429e-01,  6.391244449e-01,
   6.343932842e-01,  6.296382389e-01,  6.248594881e-01,  6.200572118e-01,
   6.152315906e-01,  6.103828063e-01,  6.055110414e-01,  6.006164794e-01,
   5.956993045e-01,  5.907597019e-01,  5.857978575e-01,  5.808139581e-01,
   5.758081914e-01,  5.707807459e-01,  5.657318108e-01,  5.606615762e-01,
   5.555702330e-01,  5.504579729e-01,  5.453249884e-01,  5.401714727e-01,
   5.349976199e-01,  5.298036247e-01,  5.245896827e-01,  5.193559902e-01,
   5.141027442e-01,  5.088301425e-01,  5.035383837e-01,  4.982276670e-01,
   4.928981922e-01,  4.875501601e-01,  4.821837721e-01,  4.767992301e-01,
   4.713967368e-01,  4.659764958e-01,  4.605387110e-01,  4.550835871e-01,
   4.496113297e-01,  4.441221446e-01,  4.386162385e-01,  4.330938189e-01,
   4.275550934e-01,  4.220002708e-01,  4.164295601e-01,  4.108431711e-01,
   4.052413140e-01,  3.996241998e-01,  3.939920401e-01,  3.883450467e-01,
   3.826834324e-01,  3.770074102e-01,  3.713171940e-01,  3.656129978e-01,
   3.598950365e-01,  3.541635254e-01,  3.484186802e-01,  3.426607173e-01,
   3.368898534e-01,  3.311063058e-01,  3.253102922e-01,  3.195020308e-01,
   3.136817404e-01,  3.078496400e-01,  3.020059493e-01,  2.961508882e-01,
   2.902846773e-01,  2.844075372e-01,  2.785196894e-01,  2.726213554e-01,
   2.667127575e-01,  2.607941179e-01,  2.548656596e-01,  2.489276057e-01,
   2.429801799e-01,  2.370236060e-01,  2.310581083e-01,  2.250839114e-01,
   2.191012402e-01,  2.131103199e-01,  2.071113762e-01,  2.011046348e-01,
   1.950903220e-01,  1.890686641e-01,  1.830398880e-01,  1.770042204e-01,
   1.709618888e-01,  1.649131205e-01,  1.588581433e-01,  1.527971853e-01,
   1.467304745e-01,  1.406582393e-01,  1.345807085e-01,  1.284981108e-01,
   1.224106752e-01,  1.163186309e-01,  1.102222073e-01,  1.041216339e-01,
   9.801714033e-02,  9.190895650e-02,  8.579731234e-02,  7.968243797e-02,
   7.356456360e-02,  6.744391956e-02,  6.132073630e-02,  5.519524435e-02,
   4.906767433e-02,  4.293825693e-02,  3.680722294e-02,  3.067480318e-02,
   2.454122852e-02,  1.840672991e-02,  1.227153829e-02,  6.135884649e-03,
   1.224646799e-16, -6.135884649e-03, -1.227153829e-02, -1.840672991e-02,
  -2.454122852e-02, -3.067480318e-02, -3.680722294e-02, -4.293825693e-02,
  -4.906767433e-02, -5.519524435e-02, -6.132073630e-02, -6.744391956e-02,
  -7.356456360e-02, -7.968243797e-02, -8.579731234e-02, -9.190895650e-02,
  -9.801714033e-02, -1.041216339e-01, -1.102222073e-01, -1.163186309e-01,
  -1.224106752e-01, -1.284981108e-01, -1.345807085e-01, -1.406582393e-01,
  -1.467304745e-01, -1.527971853e-01, -1.588581433e-01, -1.649131205e-01,
  -1.709618888e-01, -1.770042204e-01, -1.830398880e-01, -1.890686641e-01,
  -1.950903220e-01, -2.011046348e-01, -2.071113762e-01, -2.131103199e-01,
  -2.191012402e-01, -2.250839114e-01, -2.310581083e-01, -2.370236060e-01,
  -2.429801799e-01, -2.489276057e-01, -2.548656596e-01, -2.607941179e-01,
  -2.667127575e-01, -2.726213554e-01, -2.785196894e-01, -2.844075372e-01,
  -2.902846773e-01, -2.961508882e-01, -3.020059493e-01, -3.078496400e-01,
  -3.136817404e-01, -3.195020308e-01, -3.253102922e-01, -3.311063058e-01,
  -3.368898534e-01, -3.426607173e-01, -3.484186802e-01, -3.541635254e-01,
  -3.598950365e-01, -3.656129978e-01, -3.713171940e-01, -3.770074102e-01,
  -3.826834324e-01, -3.883450467e-01, -3.939920401e-01, -3.996241998e-01,
  -4.052413140e-01, -4.108431711e-01, -4.164295601e-01, -4.220002708e-01,
  -4.275550934e-01, -4.330938189e-01, -4.386162385e-01, -4.441221446e-01,
  -4.496113297e-01, -4.550835871e-01, -4.605387110e-01, -4.659764958e-01,
  -4.713967368e-01, -4.767992301e-01, -4.821837721e-01, -4.875501601e-01,
  -4.928981922e-01, -4.982276670e-01, -5.035383837e-01, -5.088301425e-01,
  -5.141027442e-01, -5.193559902e-01, -5.245896827e-01, -5.298036247e-01,
  -5.349976199e-01, -5.401714727e-01, -5.453249884e-01, -5.504579729e-01,
  -5.555702330e-01, -5.606615762e-01, -5.657318108e-01, -5.707807459e-01,
  -5.758081914e-01, -5.808139581e-01, -5.857978575e-01, -5.907597019e-01,
  -5.956993045e-01, -6.006164794e-01, -6.055110414e-01, -6.103828063e-01,
  -6.152315906e-01, -6.200572118e-01, -6.248594881e-01, -6.296382389e-01,
  -6.343932842e-01, -6.391244449e-01, -6.438315429e-01, -6.485144010e-01,
  -6.531728430e-01, -6.578066933e-01, -6.624157776e-01, -6.669999223e-01,
  -6.715589548e-01, -6.760927036e-01, -6.806009978e-01, -6.850836678e-01,
  -6.895405447e-01, -6.939714609e-01, -6.983762494e-01, -7.027547445e-01,
  -7.071067812e-01, -7.114321957e-01, -7.157308253e-01, -7.200025080e-01,
  -7.242470830e-01, -7.284643904e-01, -7.326542717e-01, -7.368165689e-01,
  -7.409511254e-01, -7.450577854e-01, -7.491363945e-01, -7.531867990e-01,
  -7.572088465e-01, -7.612023855e-01, -7.651672656e-01, -7.691033376e-01,
  -7.730104534e-01, -7.768884657e-01, -7.807372286e-01, -7.845565972e-01,
  -7.883464276e-01, -7.921065773e-01, -7.958369046e-01, -7.995372691e-01,
  -8.032075315e-01, -8.068475535e-01, -8.104571983e-01, -8.140363297e-01,
  -8.175848132e-01, -8.211025150e-01, -8.245893028e-01, -8.280450453e-01,
  -8.314696123e-01, -8.348628750e-01, -8.382247056e-01, -8.415549774e-01,
  -8.448535652e-01, -8.481203448e-01, -8.513551931e-01, -8.545579884e-01,
  -8.577286100e-01, -8.608669386e-01, -8.639728561e-01, -8.670462455e-01,
  -8.700869911e-01, -8.730949784e-01, -8.760700942e-01, -8.790122264e-01,
  -8.819212643e-01, -8.847970984e-01, -8.876396204e-01, -8.904487232e-01,
  -8.932243012e-01, -8.959662498e-01, -8.986744657e-01, -9.013488470e-01,
  -9.039892931e-01, -9.065957045e-01, -9.091679831e-01, -9.117060320e-01,
  -9.142097557e-01, -9.166790599e-01, -9.191138517e-01, -9.215140393e-01,
  -9.238795325e-01, -9.262102421e-01, -9.285060805e-01, -9.307669611e-01,
  -9.329927988e-01, -9.351835099e-01, -9.373390119e-01, -9.394592236e-01,
  -9.415440652e-01, -9.435934582e-01, -9.456073254e-01, -9.475855910e-01,
  -9.495281806e-01, -9.514350210e-01, -9.533060404e-01, -9.551411683e-01,
  -9.569403357e-01, -9.587034749e-01, -9.604305194e-01, -9.621214043e-01,
  -9.637760658e-01, -9.653944417e-01, -9.669764710e-01, -9.685220943e-01,
  -9.700312532e-01, -9.715038910e-01, -9.729399522e-01, -9.743393828e-01,
  -9.757021300e-01, -9.770281427e-01, -9.783173707e-01, -9.795697657e-01,
  -9.807852804e-01, -9.819638691e-01, -9.831054874e-01, -9.842100924e-01,
  -9.852776424e-01, -9.863080972e-01, -9.873014182e-01, -9.882575677e-01,
  -9.891765100e-01, -9.900582103e-01, -9.909026354e-01, -9.917097537e-01,
  -9.924795346e-01, -9.932119492e-01, -9.939069700e-01, -9.945645707e-01,
  -9.951847267e-01, -9.957674145e-01, -9.963126122e-01, -9.968202993e-01,
  -9.972904567e-01, -9.977230666e-01, -9.981181129e-01, -9.984755806e-01,
  -9.987954562e-01, -9.990777278e-01, -9.993223846e-01, -9.995294175e-01,
  -9.996988187e-01, -9.998305818e-01, -9.999247018e-01, -9.999811753e-01,
  -1.000000000e+00, -9.999811753e-01, -9.999247018e-01, -9.998305818e-01,
  -9.996988187e-01, -9.995294175e-01, -9.993223846e-01, -9.990777278e-01,
  -9.987954562e-01, -9.984755806e-01, -9.981181129e-01, -9.977230666e-01,
  -9.972904567e-01, -9.968202993e-01, -9.963126122e-01, -9.957674145e-01,
  -9.951847267e-01, -9.945645707e-01, -9.939069700e-01, -9.932119492e-01,
  -9.924795346e-01, -9.917097537e-01, -9.909026354e-01, -9.900582103e-01,
  -9.891765100e-01, -9.882575677e-01, -9.873014182e-01, -9.863080972e-01,
  -9.852776424e-01, -9.842100924e-01, -9.831054874e-01, -9.819638691e-01,
  -9.807852804e-01, -9.795697657e-01, -9.783173707e-01, -9.770281427e-01,
  -9.757021300e-01, -9.743393828e-01, -9.729399522e-01, -9.715038910e-01,
  -9.700312532e-01, -9.685220943e-01, -9.669764710e-01, -9.653944417e-01,
  -9.637760658e-01, -9.621214043e-01, -9.604305194e-01, -9.587034749e-01,
  -9.569403357e-01, -9.551411683e-01, -9.533060404e-01, -9.514350210e-01,
  -9.495281806e-01, -9.475855910e-01, -9.456073254e-01, -9.435934582e-01,
  -9.415440652e-01, -9.394592236e-01, -9.373390119e-01, -9.351835099e-01,
  -9.329927988e-01, -9.307669611e-01, -9.285060805e-01, -9.262102421e-01,
  -9.238795325e-01, -9.215140393e-01, -9.191138517e-01, -9.166790599e-01,
  -9.142097557e-01, -9.117060320e-01, -9.091679831e-01, -9.065957045e-01,
  -9.039892931e-01, -9.013488470e-01, -8.986744657e-01, -8.959662498e-01,
  -8.932243012e-01, -8.904487232e-01, -8.876396204e-01, -8.847970984e-01,
  -8.819212643e-01, -8.790122264e-01, -8.760700942e-01, -8.730949784e-01,
  -8.700869911e-01, -8.670462455e-01, -8.639728561e-01, -8.608669386e-01,
  -8.577286100e-01, -8.545579884e-01, -8.513551931e-01, -8.481203448e-01,
  -8.448535652e-01, -8.415549774e-01, -8.382247056e-01, -8.348628750e-01,
  -8.314696123e-01, -8.280450453e-01, -8.245893028e-01, -8.211025150e-01,
  -8.175848132e-01, -8.140363297e-01, -8.104571983e-01, -8.068475535e-01,
  -8.032075315e-01, -7.995372691e-01, -7.958369046e-01, -7.921065773e-01,
  -7.883464276e-01, -7.845565972e-01, -7.807372286e-01, -7.768884657e-01,
  -7.730104534e-01, -7.691033376e-01, -7.651672656e-01, -7.612023855e-01,
  -7.572088465e-01, -7.531867990e-01, -7.491363945e-01, -7.450577854e-01,
  -7.409511254e-01, -7.368165689e-01, -7.326542717e-01, -7.284643904e-01,
  -7.242470830e-01, -7.200025080e-01, -7.157308253e-01, -7.114321957e-01,
  -7.071067812e-01, -7.027547445e-01, -6.983762494e-01, -6.939714609e-01,
  -6.895405447e-01, -6.850836678e-01, -6.806009978e-01, -6.760927036e-01,
  -6.715589548e-01, -6.669999223e-01, -6.624157776e-01, -6.578066933e-01,
  -6.531728430e-01, -6.485144010e-01, -6.438315429e-01, -6.391244449e-01,
  -6.343932842e-01, -6.296382389e-01, -6.248594881e-01, -6.200572118e-01,
  -6.152315906e-01, -6.103828063e-01, -6.055110414e-01, -6.006164794e-01,
  -5.956993045e-01, -5.907597019e-01, -5.857978575e-01, -5.808139581e-01,
  -5.758081914e-01, -5.707807459e-01, -5.657318108e-01, -5.606615762e-01,
  -5.555702330e-01, -5.504579729e-01, -5.453249884e-01, -5.401714727e-01,
  -5.349976199e-01, -5.298036247e-01, -5.245896827e-01, -5.193559902e-01,
  -5.141027442e-01, -5.088301425e-01, -5.035383837e-01, -4.982276670e-01,
  -4.928981922e-01, -4.875501601e-01, -4.821837721e-01, -4.767992301e-01,
  -4.713967368e-01, -4.659764958e-01, -4.605387110e-01, -4.550835871e-01,
  -4.496113297e-01, -4.441221446e-01, -4.386162385e-01, -4.330938189e-01,
  -4.275550934e-01, -4.220002708e-01, -4.164295601e-01, -4.108431711e-01,
  -4.052413140e-01, -3.996241998e-01, -3.939920401e-01, -3.883450467e-01,
  -3.826834324e-01, -3.770074102e-01, -3.713171940e-01, -3.656129978e-01,
  -3.598950365e-01, -3.541635254e-01, -3.484186802e-01, -3.426607173e-01,
  -3.368898534e-01, -3.311063058e-01, -3.253102922e-01, -3.195020308e-01,
  -3.136817404e-01, -3.078496400e-01, -3.020059493e-01, -2.961508882e-01,
  -2.902846773e-01, -2.844075372e-01, -2.785196894e-01, -2.726213554e-01,
  -2.667127575e-01, -2.607941179e-01, -2.548656596e-01, -2.489276057e-01,
  -2.429801799e-01, -2.370236060e-01, -2.310581083e-01, -2.250839114e-01,
  -2.191012402e-01, -2.131103199e-01, -2.071113762e-01, -2.011046348e-01,
  -1.950903220e-01, -1.890686641e-01, -1.830398880e-01, -1.770042204e-01,
  -1.709618888e-01, -1.649131205e-01, -1.588581433e-01, -1.527971853e-01,
  -1.467304745e-01, -1.406582393e-01, -1.345807085e-01, -1.284981108e-01,
  -1.224106752e-01, -1.163186309e-01, -1.102222073e-01, -1.041216339e-01,
  -9.801714033e-02, -9.190895650e-02, -8.579731234e-02, -7.968243797e-02,
  -7.356456360e-02, -6.744391956e-02, -6.132073630e-02, -5.519524435e-02,
  -4.906767433e-02, -4.293825693e-02, -3.680722294e-02, -3.067480318e-02,
  -2.454122852e-02, -1.840672991e-02, -1.227153829e-02, -6.135884649e-03,
  -2.449293598e-16,  6.135884649e-03,  1.227153829e-02,  1.840672991e-02,
   2.454122852e-02,  3.067480318e-02,  3.680722294e-02,  4.293825693e-02,
   4.906767433e-02,  5.519524435e-02,  6.132073630e-02,  6.744391956e-02,
   7.356456360e-02,  7.968243797e-02,  8.579731234e-02,  9.190895650e-02,
   9.801714033e-02,  1.041216339e-01,  1.102222073e-01,  1.163186309e-01,
   1.224106752e-01,  1.284981108e-01,  1.345807085e-01,  1.406582393e-01,
   1.467304745e-01,  1.527971853e-01,  1.588581433e-01,  1.649131205e-01,
   1.709618888e-01,  1.770042204e-01,  1.830398880e-01,  1.890686641e-01,
   1.950903220e-01,  2.011046348e-01,  2.071113762e-01,  2.131103199e-01,
   2.191012402e-01,  2.250839114e-01,  2.310581083e-01,  2.370236060e-01,
   2.429801799e-01,  2.489276057e-01,  2.548656596e-01,  2.607941179e-01,
   2.667127575e-01,  2.726213554e-01,  2.785196894e-01,  2.844075372e-01,
   2.902846773e-01,  2.961508882e-01,  3.020059493e-01,  3.078496400e-01,
   3.136817404e-01,  3.195020308e-01,  3.253102922e-01,  3.311063058e-01,
   3.368898534e-01,  3.426607173e-01,  3.484186802e-01,  3.541635254e-01,
   3.598950365e-01,  3.656129978e-01,  3.713171940e-01,  3.770074102e-01,
   3.826834324e-01,  3.883450467e-01,  3.939920401e-01,  3.996241998e-01,
   4.052413140e-01,  4.108431711e-01,  4.164295601e-01,  4.220002708e-01,
   4.275550934e-01,  4.330938189e-01,  4.386162385e-01,  4.441221446e-01,
   4.496113297e-01,  4.550835871e-01,  4.605387110e-01,  4.659764958e-01,
   4.713967368e-01,  4.767992301e-01,  4.821837721e-01,  4.875501601e-01,
   4.928981922e-01,  4.982276670e-01,  5.035383837e-01,  5.088301425e-01,
   5.141027442e-01,  5.193559902e-01,  5.245896827e-01,  5.298036247e-01,
   5.349976199e-01,  5.401714727e-01,  5.453249884e-01,  5.504579729e-01,
   5.555702330e-01,  5.606615762e-01,  5.657318108e-01,  5.707807459e-01,
   5.758081914e-01,  5.808139581e-01,  5.857978575e-01,  5.907597019e-01,
   5.956993045e-01,  6.006164794e-01,  6.055110414e-01,  6.103828063e-01,
   6.152315906e-01,  6.200572118e-01,  6.248594881e-01,  6.296382389e-01,
   6.343932842e-01,  6.391244449e-01,  6.438315429e-01,  6.485144010e-01,
   6.531728430e-01,  6.578066933e-01,  6.624157776e-01,  6.669999223e-01,
   6.715589548e-01,  6.760927036e-01,  6.806009978e-01,  6.850836678e-01,
   6.895405447e-01,  6.939714609e-01,  6.983762494e-01,  7.027547445e-01,
   7.071067812e-01,  7.114321957e-01,  7.157308253e-01,  7.200025080e-01,
   7.242470830e-01,  7.284643904e-01,  7.326542717e-01,  7.368165689e-01,
   7.409511254e-01,  7.450577854e-01,  7.491363945e-01,  7.531867990e-01,
   7.572088465e-01,  7.612023855e-01,  7.651672656e-01,  7.691033376e-01,
   7.730104534e-01,  7.768884657e-01,  7.807372286e-01,  7.845565972e-01,
   7.883464276e-01,  7.921065773e-01,  7.958369046e-01,  7.995372691e-01,
   8.032075315e-01,  8.068475535e-01,  8.104571983e-01,  8.140363297e-01,
   8.175848132e-01,  8.211025150e-01,  8.245893028e-01,  8.280450453e-01,
   8.314696123e-01,  8.348628750e-01,  8.382247056e-01,  8.415549774e-01,
   8.448535652e-01,  8.481203448e-01,  8.513551931e-01,  8.545579884e-01,
   8.577286100e-01,  8.608669386e-01,  8.639728561e-01,  8.670462455e-01,
   8.700869911e-01,  8.730949784e-01,  8.760700942e-01,  8.790122264e-01,
   8.819212643e-01,  8.847970984e-01,  8.876396204e-01,  8.904487232e-01,
   8.932243012e-01,  8.959662498e-01,  8.986744657e-01,  9.013488470e-01,
   9.039892931e-01,  9.065957045e-01,  9.091679831e-01,  9.117060320e-01,
   9.142097557e-01,  9.166790599e-01,  9.191138517e-01,  9.215140393e-01,
   9.238795325e-01,  9.262102421e-01,  9.285060805e-01,  9.307669611e-01,
   9.329927988e-01,  9.351835099e-01,  9.373390119e-01,  9.394592236e-01,
   9.415440652e-01,  9.435934582e-01,  9.456073254e-01,  9.475855910e-01,
   9.495281806e-01,  9.514350210e-01,  9.533060404e-01,  9.551411683e-01,
   9.569403357e-01,  9.587034749e-01,  9.604305194e-01,  9.621214043e-01,
   9.637760658e-01,  9.653944417e-01,  9.669764710e-01,  9.685220943e-01,
   9.700312532e-01,  9.715038910e-01,  9.729399522e-01,  9.743393828e-01,
   9.757021300e-01,  9.770281427e-01,  9.783173707e-01,  9.795697657e-01,
   9.807852804e-01,  9.819638691e-01,  9.831054874e-01,  9.842100924e-01,
   9.852776424e-01,  9.863080972e-01,  9.873014182e-01,  9.882575677e-01,
   9.891765100e-01,  9.900582103e-01,  9.909026354e-01,  9.917097537e-01,
   9.924795346e-01,  9.932119492e-01,  9.939069700e-01,  9.945645707e-01,
   9.951847267e-01,  9.957674145e-01,  9.963126122e-01,  9.968202993e-01,
   9.972904567e-01,  9.977230666e-01,  9.981181129e-01,  9.984755806e-01,
   9.987954562e-01,  9.990777278e-01,  9.993223846e-01,  9.995294175e-01,
   9.996988187e-01,  9.998305818e-01,  9.999247018e-01,  9.999811753e-01,
   1.000000000e+00,
};
const float lut_fm_frequency_quantizer[] = {
  -1.200000000e+01, -1.200000000e+01, -1.200000000e+01, -1.184000000e+01,
  -1.184000000e+01, -1.184000000e+01, -1.111000000e+01, -1.038000000e+01,
  -9.650000000e+00, -8.920000000e+00, -8.190000000e+00, -7.460000000e+00,
  -6.730000000e+00, -6.000000000e+00, -6.000000000e+00, -6.000000000e+00,
  -5.545511612e+00, -5.091023223e+00, -4.636534835e+00, -4.182046446e+00,
  -4.182046446e+00, -4.182046446e+00, -3.659290641e+00, -3.136534835e+00,
  -2.613779029e+00, -2.091023223e+00, -1.568267417e+00, -1.045511612e+00,
  -5.227558058e-01,  0.000000000e+00,  0.000000000e+00,  0.000000000e+00,
   1.600000000e-01,  1.600000000e-01,  1.600000000e-01,  8.900000000e-01,
   1.620000000e+00,  2.350000000e+00,  3.080000000e+00,  3.810000000e+00,
   4.540000000e+00,  5.270000000e+00,  6.000000000e+00,  6.000000000e+00,
   6.000000000e+00,  6.454488388e+00,  6.908976777e+00,  7.363465165e+00,
   7.817953554e+00,  7.817953554e+00,  7.817953554e+00,  8.285529931e+00,
   8.753106309e+00,  9.220682687e+00,  9.688259065e+00,  9.688259065e+00,
   9.688259065e+00,  1.026619430e+01,  1.084412953e+01,  1.142206477e+01,
   1.200000000e+01,  1.200000000e+01,  1.200000000e+01,  1.216000000e+01,
   1.216000000e+01,  1.216000000e+01,  1.262977500e+01,  1.309955001e+01,
   1.356932501e+01,  1.403910002e+01,  1.403910002e+01,  1.403910002e+01,
   1.490761987e+01,  1.577613972e+01,  1.664465957e+01,  1.751317942e+01,
   1.751317942e+01,  1.751317942e+01,  1.800000000e+01,  1.800000000e+01,
   1.800000000e+01,  1.850977500e+01,  1.901955001e+01,  1.901955001e+01,
   1.901955001e+01,  1.981795355e+01,  1.981795355e+01,  1.981795355e+01,
   2.066386428e+01,  2.150977500e+01,  2.150977500e+01,  2.150977500e+01,
   2.213233125e+01,  2.275488750e+01,  2.337744375e+01,  2.400000000e+01,
   2.400000000e+01,  2.400000000e+01,  2.450977500e+01,  2.501955001e+01,
   2.501955001e+01,  2.501955001e+01,  2.547403840e+01,  2.592852679e+01,
   2.638301517e+01,  2.683750356e+01,  2.683750356e+01,  2.683750356e+01,
   2.735032035e+01,  2.786313714e+01,  2.786313714e+01,  2.786313714e+01,
   2.839735285e+01,  2.893156857e+01,  2.946578428e+01,  3.000000000e+01,
   3.000000000e+01,  3.000000000e+01,  3.075000000e+01,  3.150000000e+01,
   3.225000000e+01,  3.300000000e+01,  3.375000000e+01,  3.450000000e+01,
   3.525000000e+01,  3.600000000e+01,  3.600000000e+01,  3.600000000e+01,
   3.600000000e+01,
};
const float lut_fold[] = {
  -9.980545825e-01, -9.970653772e-01, -9.960649692e-01, -9.950532582e-01,
  -9.940301939e-01, -9.929957802e-01, -9.919500809e-01, -9.908932239e-01,
  -9.898254054e-01, -9.887468930e-01, -9.876580288e-01, -9.865592310e-01,
  -9.854509946e-01, -9.843338912e-01, -9.832085672e-01, -9.820757409e-01,
  -9.809361977e-01, -9.797907840e-01, -9.786403995e-01, -9.774859869e-01,
  -9.763285207e-01, -9.751689938e-01, -9.740084017e-01, -9.728477255e-01,
  -9.716879129e-01, -9.705298570e-01, -9.693743743e-01, -9.682221804e-01,
  -9.670738649e-01, -9.659298654e-01, -9.647904408e-01, -9.636556431e-01,
  -9.625252914e-01, -9.613989436e-01, -9.602758714e-01, -9.591550347e-01,
  -9.580350590e-01, -9.569142144e-01, -9.557903981e-01, -9.546611197e-01,
  -9.535234911e-01, -9.523742208e-01, -9.512096130e-01, -9.500255727e-01,
  -9.488176173e-01, -9.475808937e-01, -9.463102039e-01, -9.450000364e-01,
  -9.436446065e-01, -9.422379038e-01, -9.407737471e-01, -9.392458479e-01,
  -9.376478811e-01, -9.359735625e-01, -9.342167345e-01, -9.323714562e-01,
  -9.304321011e-01, -9.283934575e-01, -9.262508342e-01, -9.240001674e-01,
  -9.216381294e-01, -9.191622368e-01, -9.165709565e-01, -9.138638086e-01,
  -9.110414630e-01, -9.081058297e-01, -9.050601387e-01, -9.019090092e-01,
  -8.986585056e-01, -8.953161780e-01, -8.918910851e-01, -8.883937990e-01,
  -8.848363883e-01, -8.812323792e-01, -8.775966932e-01, -8.739455595e-01,
  -8.702964016e-01, -8.666676980e-01, -8.630788161e-01, -8.595498195e-01,
  -8.561012493e-01, -8.527538811e-01, -8.495284571e-01, -8.464453973e-01,
  -8.435244910e-01, -8.407845708e-01, -8.382431741e-01, -8.359161932e-01,
  -8.338175206e-01, -8.319586927e-01, -8.303485360e-01, -8.289928229e-01,
  -8.278939413e-01, -8.270505833e-01, -8.264574602e-01, -8.261050485e-01,
  -8.259793727e-01, -8.260618323e-01, -8.263290765e-01, -8.267529332e-01,
  -8.273003972e-01, -8.279336816e-01, -8.286103366e-01, -8.292834393e-01,
  -8.299018559e-01, -8.304105799e-01, -8.307511441e-01, -8.308621097e-01,
  -8.306796276e-01, -8.301380721e-01, -8.291707415e-01, -8.277106225e-01,
  -8.256912103e-01, -8.230473793e-01, -8.197162939e-01, -8.156383519e-01,
  -8.107581485e-01, -8.050254496e-01, -7.983961624e-01, -7.908332902e-01,
  -7.823078566e-01, -7.727997861e-01, -7.622987256e-01, -7.508047928e-01,
  -7.383292372e-01, -7.248949979e-01, -7.105371474e-01, -6.953032052e-01,
  -6.792533125e-01, -6.624602549e-01, -6.450093250e-01, -6.269980173e-01,
  -6.085355495e-01, -5.897422068e-01, -5.707485064e-01, -5.516941858e-01,
  -5.327270153e-01, -5.140014423e-01, -4.956770752e-01, -4.779170191e-01,
  -4.608860753e-01, -4.447488219e-01, -4.296675951e-01, -4.158003906e-01,
  -4.032987090e-01, -3.923053718e-01, -3.829523325e-01, -3.753585132e-01,
  -3.696276948e-01, -3.658464920e-01, -3.640824427e-01, -3.643822430e-01,
  -3.667701571e-01, -3.712466318e-01, -3.777871433e-01, -3.863413015e-01,
  -3.968322361e-01, -4.091562858e-01, -4.231830080e-01, -4.387555229e-01,
  -4.556912047e-01, -4.737827239e-01, -4.927994449e-01, -5.124891750e-01,
  -5.325802587e-01, -5.527840042e-01, -5.727974254e-01, -5.923062779e-01,
  -6.109883621e-01, -6.285170609e-01, -6.445650789e-01, -6.588083399e-01,
  -6.709300033e-01, -6.806245487e-01, -6.876018827e-01, -6.915914142e-01,
  -6.923460464e-01, -6.896460314e-01, -6.833026329e-01, -6.731615438e-01,
  -6.591060076e-01, -6.410595911e-01, -6.189885640e-01, -5.929038395e-01,
  -5.628624373e-01, -5.289684349e-01, -4.913733765e-01, -4.502761195e-01,
  -4.059220990e-01, -3.586020036e-01, -3.086498600e-01, -2.564405314e-01,
  -2.023866445e-01, -1.469349657e-01, -9.056225673e-02, -3.377064458e-02,
   2.291744737e-02,  7.896475831e-02,  1.338249802e-01,  1.869488164e-01,
   2.377902398e-01,  2.858128778e-01,  3.304964479e-01,  3.713431643e-01,
   4.078840357e-01,  4.396849726e-01,  4.663526243e-01,  4.875398649e-01,
   5.029508548e-01,  5.123456023e-01,  5.155439593e-01,  5.124289894e-01,
   5.029496521e-01,  4.871227568e-01,  4.650341465e-01,  4.368390827e-01,
   4.027618100e-01,  3.630942908e-01,  3.181941105e-01,  2.684815644e-01,
   2.144359470e-01,  1.565910778e-01,  9.553010345e-02,  3.187963220e-02,
  -3.369674102e-02, -1.005054456e-01, -1.678304053e-01, -2.349408810e-01,
  -3.010995956e-01, -3.655710438e-01, -4.276298873e-01, -4.865693337e-01,
  -5.417093944e-01, -5.924049204e-01, -6.380533123e-01, -6.781018093e-01,
  -7.120542597e-01, -7.394772881e-01, -7.600057749e-01, -7.733475770e-01,
  -7.792874237e-01, -7.776899338e-01, -7.685017108e-01, -7.517524823e-01,
  -7.275552655e-01, -6.961055475e-01, -6.576794884e-01, -6.126311602e-01,
  -5.613888527e-01, -5.044504876e-01, -4.423781911e-01, -3.757920909e-01,
  -3.053634092e-01, -2.318069348e-01, -1.558729654e-01, -7.833881626e-02,
   0.000000000e+00,  7.833881626e-02,  1.558729654e-01,  2.318069348e-01,
   3.053634092e-01,  3.757920909e-01,  4.423781911e-01,  5.044504876e-01,
   5.613888527e-01,  6.126311602e-01,  6.576794884e-01,  6.961055475e-01,
   7.275552655e-01,  7.517524823e-01,  7.685017108e-01,  7.776899338e-01,
   7.792874237e-01,  7.733475770e-01,  7.600057749e-01,  7.394772881e-01,
   7.120542597e-01,  6.781018093e-01,  6.380533123e-01,  5.924049204e-01,
   5.417093944e-01,  4.865693337e-01,  4.276298873e-01,  3.655710438e-01,
   3.010995956e-01,  2.349408810e-01,  1.678304053e-01,  1.005054456e-01,
   3.369674102e-02, -3.187963220e-02, -9.553010345e-02, -1.565910778e-01,
  -2.144359470e-01, -2.684815644e-01, -3.181941105e-01, -3.630942908e-01,
  -4.027618100e-01, -4.368390827e-01, -4.650341465e-01, -4.871227568e-01,
  -5.029496521e-01, -5.124289894e-01, -5.155439593e-01, -5.123456023e-01,
  -5.029508548e-01, -4.875398649e-01, -4.663526243e-01, -4.396849726e-01,
  -4.078840357e-01, -3.713431643e-01, -3.304964479e-01, -2.858128778e-01,
  -2.377902398e-01, -1.869488164e-01, -1.338249802e-01, -7.896475831e-02,
  -2.291744737e-02,  3.377064458e-02,  9.056225673e-02,  1.469349657e-01,
   2.023866445e-01,  2.564405314e-01,  3.086498600e-01,  3.586020036e-01,
   4.059220990e-01,  4.502761195e-01,  4.913733765e-01,  5.289684349e-01,
   5.628624373e-01,  5.929038395e-01,  6.189885640e-01,  6.410595911e-01,
   6.591060076e-01,  6.731615438e-01,  6.833026329e-01,  6.896460314e-01,
   6.923460464e-01,  6.915914142e-01,  6.876018827e-01,  6.806245487e-01,
   6.709300033e-01,  6.588083399e-01,  6.445650789e-01,  6.285170609e-01,
   6.109883621e-01,  5.923062779e-01,  5.727974254e-01,  5.527840042e-01,
   5.325802587e-01,  5.124891750e-01,  4.927994449e-01,  4.737827239e-01,
   4.556912047e-01,  4.387555229e-01,  4.231830080e-01,  4.091562858e-01,
   3.968322361e-01,  3.863413015e-01,  3.777871433e-01,  3.712466318e-01,
   3.667701571e-01,  3.643822430e-01,  3.640824427e-01,  3.658464920e-01,
   3.696276948e-01,  3.753585132e-01,  3.829523325e-01,  3.923053718e-01,
   4.032987090e-01,  4.158003906e-01,  4.296675951e-01,  4.447488219e-01,
   4.608860753e-01,  4.779170191e-01,  4.956770752e-01,  5.140014423e-01,
   5.327270153e-01,  5.516941858e-01,  5.707485064e-01,  5.897422068e-01,
   6.085355495e-01,  6.269980173e-01,  6.450093250e-01,  6.624602549e-01,
   6.792533125e-01,  6.953032052e-01,  7.105371474e-01,  7.248949979e-01,
   7.383292372e-01,  7.508047928e-01,  7.622987256e-01,  7.727997861e-01,
   7.823078566e-01,  7.908332902e-01,  7.983961624e-01,  8.050254496e-01,
   8.107581485e-01,  8.156383519e-01,  8.197162939e-01,  8.230473793e-01,
   8.256912103e-01,  8.277106225e-01,  8.291707415e-01,  8.301380721e-01,
   8.306796276e-01,  8.308621097e-01,  8.307511441e-01,  8.304105799e-01,
   8.299018559e-01,  8.292834393e-01,  8.286103366e-01,  8.279336816e-01,
   8.273003972e-01,  8.267529332e-01,  8.263290765e-01,  8.260618323e-01,
   8.259793727e-01,  8.261050485e-01,  8.264574602e-01,  8.270505833e-01,
   8.278939413e-01,  8.289928229e-01,  8.303485360e-01,  8.319586927e-01,
   8.338175206e-01,  8.359161932e-01,  8.382431741e-01,  8.407845708e-01,
   8.435244910e-01,  8.464453973e-01,  8.495284571e-01,  8.527538811e-01,
   8.561012493e-01,  8.595498195e-01,  8.630788161e-01,  8.666676980e-01,
   8.702964016e-01,  8.739455595e-01,  8.775966932e-01,  8.812323792e-01,
   8.848363883e-01,  8.883937990e-01,  8.918910851e-01,  8.953161780e-01,
   8.986585056e-01,  9.019090092e-01,  9.050601387e-01,  9.081058297e-01,
   9.110414630e-01,  9.138638086e-01,  9.165709565e-01,  9.191622368e-01,
   9.216381294e-01,  9.240001674e-01,  9.262508342e-01,  9.283934575e-01,
   9.304321011e-01,  9.323714562e-01,  9.342167345e-01,  9.359735625e-01,
   9.376478811e-01,  9.392458479e-01,  9.407737471e-01,  9.422379038e-01,
   9.436446065e-01,  9.450000364e-01,  9.463102039e-01,  9.475808937e-01,
   9.488176173e-01,  9.500255727e-01,  9.512096130e-01,  9.523742208e-01,
   9.535234911e-01,  9.546611197e-01,  9.557903981e-01,  9.569142144e-01,
   9.580350590e-01,  9.591550347e-01,  9.602758714e-01,  9.613989436e-01,
   9.625252914e-01,  9.636556431e-01,  9.647904408e-01,  9.659298654e-01,
   9.670738649e-01,  9.682221804e-01,  9.693743743e-01,  9.705298570e-01,
   9.716879129e-01,  9.728477255e-01,  9.740084017e-01,  9.751689938e-01,
   9.763285207e-01,  9.774859869e-01,  9.786403995e-01,  9.797907840e-01,
   9.809361977e-01,  9.820757409e-01,  9.832085672e-01,  9.843338912e-01,
   9.854509946e-01,  9.865592310e-01,  9.876580288e-01,  9.887468930e-01,
   9.898254054e-01,  9.908932239e-01,  9.919500809e-01,  9.929957802e-01,
   9.940301939e-01,  9.950532582e-01,  9.960649692e-01,  9.970653772e-01,
   9.980545825e-01,  9.990327291e-01,  1.000000000e+00,  1.000000000e+00,
};
const float lut_fold_2[] = {
   1.000000000e+00,  9.992967758e-01,  9.985815484e-01,  9.978540078e-01,
   9.971138332e-01,  9.963606927e-01,  9.955942426e-01,  9.948141269e-01,
   9.940199768e-01,  9.932114103e-01,  9.923880310e-01,  9.915494283e-01,
   9.906951760e-01,  9.898248319e-01,  9.889379369e-01,  9.880340145e-01,
   9.871125695e-01,  9.861730874e-01,  9.852150334e-01,  9.842378513e-01,
   9.832409624e-01,  9.822237646e-01,  9.811856308e-01,  9.801259079e-01,
   9.790439155e-01,  9.779389442e-01,  9.768102539e-01,  9.756570727e-01,
   9.744785949e-01,  9.732739786e-01,  9.720423447e-01,  9.707827737e-01,
   9.694943044e-01,  9.681759305e-01,  9.668265989e-01,  9.654452060e-01,
   9.640305956e-01,  9.625815548e-01,  9.610968112e-01,  9.595750288e-01,
   9.580148040e-01,  9.564146617e-01,  9.547730501e-01,  9.530883359e-01,
   9.513587989e-01,  9.495826263e-01,  9.477579060e-01,  9.458826201e-01,
   9.439546371e-01,  9.419717041e-01,  9.399314380e-01,  9.378313157e-01,
   9.356686640e-01,  9.334406481e-01,  9.311442591e-01,  9.287763006e-01,
   9.263333739e-01,  9.238118615e-01,  9.212079094e-01,  9.185174075e-01,
   9.157359677e-01,  9.128589003e-01,  9.098811874e-01,  9.067974538e-01,
   9.036019347e-01,  9.002884395e-01,  8.968503119e-01,  8.932803854e-01,
   8.895709331e-01,  8.857136124e-01,  8.816994016e-01,  8.775185304e-01,
   8.731603996e-01,  8.686134921e-01,  8.638652705e-01,  8.589020627e-01,
   8.537089293e-01,  8.482695142e-01,  8.425658723e-01,  8.365782715e-01,
   8.302849649e-01,  8.236619269e-01,  8.166825462e-01,  8.093172692e-01,
   8.015331811e-01,  7.932935143e-01,  7.845570677e-01,  7.752775176e-01,
   7.654025961e-01,  7.548731062e-01,  7.436217337e-01,  7.315716072e-01,
   7.186345391e-01,  7.047088637e-01,  6.896767601e-01,  6.734009108e-01,
   6.557202943e-01,  6.364448402e-01,  6.153485688e-01,  5.921606903e-01,
   5.665539193e-01,  5.381289295e-01,  5.063933787e-01,  4.707331500e-01,
   4.303722225e-01,  3.843155503e-01,  3.312659247e-01,  2.694998552e-01,
   1.966767932e-01,  1.095358294e-01,  3.393987745e-03, -1.040028802e-01,
  -1.920923242e-01, -2.656393469e-01, -3.279705091e-01, -3.814696578e-01,
  -4.278897766e-01, -4.685487258e-01, -5.044563616e-01, -5.363995499e-01,
  -5.650004958e-01, -5.676277376e-01, -5.456089430e-01, -5.216251172e-01,
  -4.954009254e-01, -4.666070735e-01, -4.348464092e-01, -3.996354923e-01,
  -3.603798149e-01, -3.163399611e-01, -2.665845916e-01, -2.099238522e-01,
  -1.448129904e-01, -6.920937281e-02,  1.895794740e-02,  1.019348852e-01,
   1.729075540e-01,  2.343052184e-01,  2.879430943e-01,  3.352048344e-01,
   3.771635871e-01,  4.146644691e-01,  4.483820782e-01,  4.788614349e-01,
   5.065476686e-01,  5.318078998e-01,  5.549476117e-01,  5.762230650e-01,
   5.958508275e-01,  6.140151734e-01,  6.308738858e-01,  6.465628523e-01,
   6.611997355e-01,  6.748869294e-01,  6.877139581e-01,  6.925931401e-01,
   6.755415987e-01,  6.569329565e-01,  6.365437238e-01,  6.141054921e-01,
   5.892930521e-01,  5.617085284e-01,  5.308598832e-01,  4.961313087e-01,
   4.567416977e-01,  4.116851906e-01,  3.596440735e-01,  2.988577649e-01,
   2.269196964e-01,  1.404511108e-01,  3.455499060e-02, -8.308691439e-02,
  -1.798594632e-01, -2.595549970e-01, -3.263272740e-01, -3.830839556e-01,
  -4.319212812e-01, -4.743886570e-01, -5.116560503e-01, -5.446234410e-01,
  -5.739944533e-01, -6.003271365e-01, -6.109475507e-01, -5.895686806e-01,
  -5.661619434e-01, -5.404244477e-01, -5.119898195e-01, -4.804106515e-01,
  -4.451347882e-01, -4.054727657e-01, -3.605522997e-01, -3.092533873e-01,
  -2.501136501e-01, -1.811866822e-01, -9.982372580e-02, -2.325458569e-03,
   9.596728942e-02,  1.779431078e-01,  2.473476588e-01,  3.068667711e-01,
   3.584720417e-01,  4.036434517e-01,  4.435136052e-01,  4.789639990e-01,
   5.106909591e-01,  5.392518362e-01,  5.650980300e-01,  5.885990231e-01,
   6.100601564e-01,  6.297359696e-01,  6.478403436e-01,  6.645543074e-01,
   6.585194180e-01,  6.406121537e-01,  6.211278553e-01,  5.998486007e-01,
   5.765143776e-01,  5.508124062e-01,  5.223630380e-01,  4.907008769e-01,
   4.552491217e-01,  4.152841095e-01,  3.698853971e-01,  3.178639957e-01,
   2.576567279e-01,  1.871664560e-01,  1.035128010e-01,  2.628828896e-03,
  -9.918255595e-02, -1.835455764e-01, -2.545841775e-01, -3.152240342e-01,
  -3.675927060e-01, -4.132744159e-01, -4.534730876e-01, -4.891200006e-01,
  -5.209468346e-01, -5.495364245e-01, -5.753587781e-01, -5.987971175e-01,
  -6.201670260e-01, -6.397307408e-01, -6.255537426e-01, -6.058657960e-01,
  -5.844073505e-01, -5.609283358e-01, -5.351292603e-01, -5.066483683e-01,
  -4.750445715e-01, -4.397744409e-01, -4.001606981e-01, -3.553483015e-01,
  -3.042420289e-01, -2.454157756e-01, -1.769773894e-01, -9.636135435e-02,
   0.000000000e+00,  9.636135435e-02,  1.769773894e-01,  2.454157756e-01,
   3.042420289e-01,  3.553483015e-01,  4.001606981e-01,  4.397744409e-01,
   4.750445715e-01,  5.066483683e-01,  5.351292603e-01,  5.609283358e-01,
   5.844073505e-01,  6.058657960e-01,  6.255537426e-01,  6.397307408e-01,
   6.201670260e-01,  5.987971175e-01,  5.753587781e-01,  5.495364245e-01,
   5.209468346e-01,  4.891200006e-01,  4.534730876e-01,  4.132744159e-01,
   3.675927060e-01,  3.152240342e-01,  2.545841775e-01,  1.835455764e-01,
   9.918255595e-02, -2.628828896e-03, -1.035128010e-01, -1.871664560e-01,
  -2.576567279e-01, -3.178639957e-01, -3.698853971e-01, -4.152841095e-01,
  -4.552491217e-01, -4.907008769e-01, -5.223630380e-01, -5.508124062e-01,
  -5.765143776e-01, -5.998486007e-01, -6.211278553e-01, -6.406121537e-01,
  -6.585194180e-01, -6.645543074e-01, -6.478403436e-01, -6.297359696e-01,
  -6.100601564e-01, -5.885990231e-01, -5.650980300e-01, -5.392518362e-01,
  -5.106909591e-01, -4.789639990e-01, -4.435136052e-01, -4.036434517e-01,
  -3.584720417e-01, -3.068667711e-01, -2.473476588e-01, -1.779431078e-01,
  -9.596728942e-02,  2.325458569e-03,  9.982372580e-02,  1.811866822e-01,
   2.501136501e-01,  3.092533873e-01,  3.605522997e-01,  4.054727657e-01,
   4.451347882e-01,  4.804106515e-01,  5.119898195e-01,  5.404244477e-01,
   5.661619434e-01,  5.895686806e-01,  6.109475507e-01,  6.003271365e-01,
   5.739944533e-01,  5.446234410e-01,  5.116560503e-01,  4.743886570e-01,
   4.319212812e-01,  3.830839556e-01,  3.263272740e-01,  2.595549970e-01,
   1.798594632e-01,  8.308691439e-02, -3.455499060e-02, -1.404511108e-01,
  -2.269196964e-01, -2.988577649e-01, -3.596440735e-01, -4.116851906e-01,
  -4.567416977e-01, -4.961313087e-01, -5.308598832e-01, -5.617085284e-01,
  -5.892930521e-01, -6.141054921e-01, -6.365437238e-01, -6.569329565e-01,
  -6.755415987e-01, -6.925931401e-01, -6.877139581e-01, -6.748869294e-01,
  -6.611997355e-01, -6.465628523e-01, -6.308738858e-01, -6.140151734e-01,
  -5.958508275e-01, -5.762230650e-01, -5.549476117e-01, -5.318078998e-01,
  -5.065476686e-01, -4.788614349e-01, -4.483820782e-01, -4.146644691e-01,
  -3.771635871e-01, -3.352048344e-01, -2.879430943e-01, -2.343052184e-01,
  -1.729075540e-01, -1.019348852e-01, -1.895794740e-02,  6.920937281e-02,
   1.448129904e-01,  2.099238522e-01,  2.665845916e-01,  3.163399611e-01,
   3.603798149e-01,  3.996354923e-01,  4.348464092e-01,  4.666070735e-01,
   4.954009254e-01,  5.216251172e-01,  5.456089430e-01,  5.676277376e-01,
   5.650004958e-01,  5.363995499e-01,  5.044563616e-01,  4.685487258e-01,
   4.278897766e-01,  3.814696578e-01,  3.279705091e-01,  2.656393469e-01,
   1.920923242e-01,  1.040028802e-01, -3.393987745e-03, -1.095358294e-01,
  -1.966767932e-01, -2.694998552e-01, -3.312659247e-01, -3.843155503e-01,
  -4.303722225e-01, -4.707331500e-01, -5.063933787e-01, -5.381289295e-01,
  -5.665539193e-01, -5.921606903e-01, -6.153485688e-01, -6.364448402e-01,
  -6.557202943e-01, -6.734009108e-01, -6.896767601e-01, -7.047088637e-01,
  -7.186345391e-01, -7.315716072e-01, -7.436217337e-01, -7.548731062e-01,
  -7.654025961e-01, -7.752775176e-01, -7.845570677e-01, -7.932935143e-01,
  -8.015331811e-01, -8.093172692e-01, -8.166825462e-01, -8.236619269e-01,
  -8.302849649e-01, -8.365782715e-01, -8.425658723e-01, -8.482695142e-01,
  -8.537089293e-01, -8.589020627e-01, -8.638652705e-01, -8.686134921e-01,
  -8.731603996e-01, -8.775185304e-01, -8.816994016e-01, -8.857136124e-01,
  -8.895709331e-01, -8.932803854e-01, -8.968503119e-01, -9.002884395e-01,
  -9.036019347e-01, -9.067974538e-01, -9.098811874e-01, -9.128589003e-01,
  -9.157359677e-01, -9.185174075e-01, -9.212079094e-01, -9.238118615e-01,
  -9.263333739e-01, -9.287763006e-01, -9.311442591e-01, -9.334406481e-01,
  -9.356686640e-01, -9.378313157e-01, -9.399314380e-01, -9.419717041e-01,
  -9.439546371e-01, -9.458826201e-01, -9.477579060e-01, -9.495826263e-01,
  -9.513587989e-01, -9.530883359e-01, -9.547730501e-01, -9.564146617e-01,
  -9.580148040e-01, -9.595750288e-01, -9.610968112e-01, -9.625815548e-01,
  -9.640305956e-01, -9.654452060e-01, -9.668265989e-01, -9.681759305e-01,
  -9.694943044e-01, -9.707827737e-01, -9.720423447e-01, -9.732739786e-01,
  -9.744785949e-01, -9.756570727e-01, -9.768102539e-01, -9.779389442e-01,
  -9.790439155e-01, -9.801259079e-01, -9.811856308e-01, -9.822237646e-01,
  -9.832409624e-01, -9.842378513e-01, -9.852150334e-01, -9.861730874e-01,
  -9.871125695e-01, -9.880340145e-01, -9.889379369e-01, -9.898248319e-01,
  -9.906951760e-01, -9.915494283e-01, -9.923880310e-01, -9.932114103e-01,
  -9.940199768e-01, -9.948141269e-01, -9.955942426e-01, -9.963606927e-01,
  -9.971138332e-01, -9.978540078e-01, -9.985815484e-01, -9.992967758e-01,
  -1.000000000e+00, -1.000691521e+00, -1.001371627e+00, -1.001371627e+00,
};
const float lut_stiffness[] = {
  -6.250000000e-02, -5.859375000e-02, -5.468750000e-02, -5.078125000e-02,
  -4.687500000e-02, -4.296875000e-02, -3.906250000e-02, -3.515625000e-02,
  -3.125000000e-02, -2.734375000e-02, -2.343750000e-02, -1.953125000e-02,
  -1.562500000e-02, -1.171875000e-02, -7.812500000e-03, -3.906250000e-03,
   0.000000000e+00,  0.000000000e+00,  0.000000000e+00,  0.000000000e+00,
   1.009582073e-03,  2.416076364e-03,  4.002252878e-03,  5.791066350e-03,
   7.808404022e-03,  1.008346028e-02,  1.264915914e-02,  1.554263074e-02,
   1.880574864e-02,  2.248573583e-02,  2.663584813e-02,  3.131614488e-02,
   3.659435812e-02,  4.254687278e-02,  4.925983210e-02,  5.683038428e-02,
   6.536808837e-02,  7.499649981e-02,  8.585495846e-02,  9.810060511e-02,
   1.119106556e-01,  1.274849653e-01,  1.450489216e-01,  1.648567056e-01,
   1.871949702e-01,  2.123869891e-01,  2.407973346e-01,  2.728371538e-01,
   3.089701187e-01,  3.497191360e-01,  3.956739150e-01,  4.474995013e-01,
   5.059459012e-01,  5.718589358e-01,  6.461924814e-01,  7.300222738e-01,
   8.245614757e-01,  9.311782340e-01,  1.000037649e+00,  1.005639154e+00,
   1.048005353e+00,  1.183990632e+00,  1.457101344e+00,  2.000000000e+00,
   2.000000000e+00,
};
const float lut_svf_shift[] = {
   7.500000000e-01,  7.591880421e-01,  7.683455389e-01,  7.774424499e-01,
   7.864497239e-01,  7.953397451e-01,  8.040867240e-01,  8.126670211e-01,
   8.210593968e-01,  8.292451828e-01,  8.372083767e-01,  8.449356653e-01,
   8.524163823e-01,  8.596424124e-01,  8.666080494e-01,  8.733098228e-01,
   8.797462999e-01,  8.859178746e-01,  8.918265520e-01,  8.974757332e-01,
   9.028700082e-01,  9.080149595e-01,  9.129169800e-01,  9.175831064e-01,
   9.220208696e-01,  9.262381615e-01,  9.302431183e-01,  9.340440198e-01,
   9.376492031e-01,  9.410669892e-01,  9.443056230e-01,  9.473732226e-01,
   9.502777394e-01,  9.530269262e-01,  9.556283121e-01,  9.580891845e-01,
   9.604165758e-01,  9.626172547e-01,  9.646977214e-01,  9.666642057e-01,
   9.685226683e-01,  9.702788030e-01,  9.719380415e-01,  9.735055596e-01,
   9.749862835e-01,  9.763848977e-01,  9.777058532e-01,  9.789533760e-01,
   9.801314757e-01,  9.812439545e-01,  9.822944161e-01,  9.832862746e-01,
   9.842227627e-01,  9.851069409e-01,  9.859417053e-01,  9.867297957e-01,
   9.874738036e-01,  9.881761792e-01,  9.888392394e-01,  9.894651739e-01,
   9.900560522e-01,  9.906138300e-01,  9.911403551e-01,  9.916373732e-01,
   9.921065333e-01,  9.925493929e-01,  9.929674233e-01,  9.933620136e-01,
   9.937344761e-01,  9.940860496e-01,  9.944179041e-01,  9.947311441e-01,
   9.950268127e-01,  9.953058946e-01,  9.955693195e-01,  9.958179650e-01,
   9.960526598e-01,  9.962741861e-01,  9.964832825e-01,  9.966806459e-01,
   9.968669346e-01,  9.970427696e-01,  9.972087374e-01,  9.973653916e-01,
   9.975132546e-01,  9.976528197e-01,  9.977845524e-01,  9.979088923e-01,
   9.980262540e-01,  9.981370293e-01,  9.982415876e-01,  9.983402778e-01,
   9.984334293e-01,  9.985213529e-01,  9.986043419e-01,  9.986826732e-01,
   9.987566083e-01,  9.988263939e-01,  9.988922628e-01,  9.989544348e-01,
   9.990131175e-01,  9.990685067e-01,  9.991207871e-01,  9.991701333e-01,
   9.992167099e-01,  9.992606725e-01,  9.993021676e-01,  9.993413338e-01,
   9.993783018e-01,  9.994131950e-01,  9.994461297e-01,  9.994772160e-01,
   9.995065576e-01,  9.995342523e-01,  9.995603927e-01,  9.995850659e-01,
   9.996083544e-01,  9.996303357e-01,  9.996510834e-01,  9.996706665e-01,
   9.996891506e-01,  9.997065972e-01,  9.997230647e-01,  9.997386078e-01,
   9.997532786e-01,  9.997671260e-01,  9.997801962e-01,  9.997925329e-01,
   9.998041771e-01,  9.998151678e-01,  9.998255416e-01,  9.998353332e-01,
   9.998445753e-01,  9.998532986e-01,  9.998615323e-01,  9.998693039e-01,
   9.998766393e-01,  9.998835630e-01,  9.998900981e-01,  9.998962664e-01,
   9.999020885e-01,  9.999075839e-01,  9.999127708e-01,  9.999176666e-01,
   9.999222876e-01,  9.999266493e-01,  9.999307661e-01,  9.999346519e-01,
   9.999383196e-01,  9.999417815e-01,  9.999450491e-01,  9.999481332e-01,
   9.999510443e-01,  9.999537919e-01,  9.999563854e-01,  9.999588333e-01,
   9.999611438e-01,  9.999633246e-01,  9.999653831e-01,  9.999673260e-01,
   9.999691598e-01,  9.999708907e-01,  9.999725245e-01,  9.999740666e-01,
   9.999755221e-01,  9.999768960e-01,  9.999781927e-01,  9.999794167e-01,
   9.999805719e-01,  9.999816623e-01,  9.999826915e-01,  9.999836630e-01,
   9.999845799e-01,  9.999854454e-01,  9.999862623e-01,  9.999870333e-01,
   9.999877611e-01,  9.999884480e-01,  9.999890964e-01,  9.999897083e-01,
   9.999902860e-01,  9.999908312e-01,  9.999913458e-01,  9.999918315e-01,
   9.999922900e-01,  9.999927227e-01,  9.999931311e-01,  9.999935167e-01,
   9.999938805e-01,  9.999942240e-01,  9.999945482e-01,  9.999948542e-01,
   9.999951430e-01,  9.999954156e-01,  9.999956729e-01,  9.999959157e-01,
   9.999961450e-01,  9.999963613e-01,  9.999965656e-01,  9.999967583e-01,
   9.999969403e-01,  9.999971120e-01,  9.999972741e-01,  9.999974271e-01,
   9.999975715e-01,  9.999977078e-01,  9.999978364e-01,  9.999979579e-01,
   9.999980725e-01,  9.999981807e-01,  9.999982828e-01,  9.999983792e-01,
   9.999984701e-01,  9.999985560e-01,  9.999986370e-01,  9.999987135e-01,
   9.999987857e-01,  9.999988539e-01,  9.999989182e-01,  9.999989789e-01,
   9.999990362e-01,  9.999990903e-01,  9.999991414e-01,  9.999991896e-01,
   9.999992351e-01,  9.999992780e-01,  9.999993185e-01,  9.999993568e-01,
   9.999993929e-01,  9.999994269e-01,  9.999994591e-01,  9.999994895e-01,
   9.999995181e-01,  9.999995452e-01,  9.999995707e-01,  9.999995948e-01,
   9.999996175e-01,  9.999996390e-01,  9.999996593e-01,  9.999996784e-01,
   9.999996964e-01,  9.999997135e-01,  9.999997296e-01,  9.999997447e-01,
   9.999997591e-01,  9.999997726e-01,  9.999997853e-01,  9.999997974e-01,
   9.999998088e-01,  9.999998195e-01,  9.999998296e-01,  9.999998392e-01,
   9.999998482e-01,  9.999998567e-01,  9.999998648e-01,  9.999998724e-01,
   9.999998795e-01,
};


const float* lookup_table_table[] = {
  lut_sine,
  lut_fm_frequency_quantizer,
  lut_fold,
  lut_fold_2,
  lut_stiffness,
  lut_svf_shift,
};

const int16_t lut_ws_inverse_tan[] = {
  -32767, -26872, -24921, -23661,
  -22748, -22047, -21486, -21026,
  -20640, -20310, -20025, -19775,
  -19554, -19358, -19181, -19021,
  -18875, -18742, -18620, -18507,
  -18402, -18304, -18213, -18128,
  -18047, -17971, -17900, -17832,
  -17767, -17706, -17647, -17591,
  -17537, -17485, -17435, -17387,
  -17341, -17296, -17253, -17211,
  -17170, -17130, -17092, -17054,
  -17017, -16981, -16945, -16911,
  -16877, -16843, -16810, -16778,
  -16746, -16715, -16683, -16652,
  -16622, -16592, -16561, -16531,
  -16502, -16472, -16442, -16413,
  -16384, -16354, -16325, -16295,
  -16265, -16236, -16206, -16175,
  -16145, -16115, -16084, -16052,
  -16021, -15989, -15957, -15924,
  -15890, -15856, -15822, -15786,
  -15750, -15713, -15675, -15637,
  -15597, -15556, -15514, -15471,
  -15426, -15380, -15332, -15282,
  -15230, -15176, -15120, -15061,
  -15000, -14935, -14867, -14796,
  -14720, -14639, -14554, -14463,
  -14365, -14260, -14147, -14025,
  -13892, -13746, -13586, -13409,
  -13213, -12992, -12742, -12457,
  -12127, -11741, -11281, -10720,
  -10019,  -9106,  -7846,  -5895,
       0,   5895,   7846,   9106,
   10019,  10720,  11281,  11741,
   12127,  12457,  12742,  12992,
   13213,  13409,  13586,  13746,
   13892,  14025,  14147,  14260,
   14365,  14463,  14554,  14639,
   14720,  14796,  14867,  14935,
   15000,  15061,  15120,  15176,
   15230,  15282,  15332,  15380,
   15426,  15471,  15514,  15556,
   15597,  15637,  15675,  15713,
   15750,  15786,  15822,  15856,
   15890,  15924,  15957,  15989,
   16021,  16052,  16084,  16115,
   16145,  16175,  16206,  16236,
   16265,  16295,  16325,  16354,
   16384,  16413,  16442,  16472,
   16502,  16531,  16561,  16592,
   16622,  16652,  16683,  16715,
   16746,  16778,  16810,  16843,
   16877,  16911,  16945,  16981,
   17017,  17054,  17092,  17130,
   17170,  17211,  17253,  17296,
   17341,  17387,  17435,  17485,
   17537,  17591,  17647,  17706,
   17767,  17832,  17900,  17971,
   18047,  18128,  18213,  18304,
   18402,  18507,  18620,  18742,
   18875,  19021,  19181,  19358,
   19554,  19775,  20025,  20310,
   20640,  21026,  21486,  22047,
   22748,  23661,  24921,  26872,
   32767,
};
const int16_t lut_ws_inverse_sin[] = {
  -32767, -30921, -30153, -29561,
  -29060, -28617, -28215, -27843,
  -27496, -27169, -26858, -26561,
  -26276, -26001, -25736, -25479,
  -25229, -24986, -24748, -24517,
  -24290, -24068, -23850, -23636,
  -23425, -23218, -23014, -22813,
  -22614, -22419, -22225, -22034,
  -21845, -21657, -21472, -21288,
  -21106, -20926, -20747, -20569,
  -20393, -20218, -20043, -19870,
  -19698, -19527, -19357, -19188,
  -19019, -18851, -18684, -18517,
  -18351, -18185, -18020, -17855,
  -17691, -17527, -17363, -17199,
  -17036, -16873, -16709, -16546,
  -16384, -16221, -16058, -15894,
  -15731, -15568, -15404, -15240,
  -15076, -14912, -14747, -14582,
  -14416, -14250, -14083, -13916,
  -13748, -13579, -13410, -13240,
  -13069, -12897, -12724, -12549,
  -12374, -12198, -12020, -11841,
  -11661, -11479, -11295, -11110,
  -10922, -10733, -10542, -10348,
  -10153,  -9954,  -9753,  -9549,
   -9342,  -9131,  -8917,  -8699,
   -8477,  -8250,  -8019,  -7781,
   -7538,  -7288,  -7031,  -6766,
   -6491,  -6206,  -5909,  -5598,
   -5271,  -4924,  -4552,  -4150,
   -3707,  -3206,  -2614,  -1846,
       0,   1846,   2614,   3206,
    3707,   4150,   4552,   4924,
    5271,   5598,   5909,   6206,
    6491,   6766,   7031,   7288,
    7538,   7781,   8019,   8250,
    8477,   8699,   8917,   9131,
    9342,   9549,   9753,   9954,
   10153,  10348,  10542,  10733,
   10922,  11110,  11295,  11479,
   11661,  11841,  12020,  12198,
   12374,  12549,  12724,  12897,
   13069,  13240,  13410,  13579,
   13748,  13916,  14083,  14250,
   14416,  14582,  14747,  14912,
   15076,  15240,  15404,  15568,
   15731,  15894,  16058,  16221,
   16384,  16546,  16709,  16873,
   17036,  17199,  17363,  17527,
   17691,  17855,  18020,  18185,
   18351,  18517,  18684,  18851,
   19019,  19188,  19357,  19527,
   19698,  19870,  20043,  20218,
   20393,  20569,  20747,  20926,
   21106,  21288,  21472,  21657,
   21845,  22034,  22225,  22419,
   22614,  22813,  23014,  23218,
   23425,  23636,  23850,  24068,
   24290,  24517,  24748,  24986,
   25229,  25479,  25736,  26001,
   26276,  26561,  26858,  27169,
   27496,  27843,  28215,  28617,
   29060,  29561,  30153,  30921,
   32767,
};
const int16_t lut_ws_linear[] = {
  -32767, -32511, -32255, -31999,
  -31743, -31487, -31231, -30975,
  -30719, -30463, -30207, -29951,
  -29695, -29439, -29183, -28927,
  -28671, -28415, -28159, -27903,
  -27647, -27391, -27135, -26879,
  -26623, -26367, -26111, -25855,
  -25599, -25343, -25087, -24831,
  -24575, -24319, -24063, -23807,
  -23551, -23295, -23039, -22783,
  -22527, -22271, -22015, -21759,
  -21503, -21247, -20991, -20735,
  -20479, -20223, -19967, -19711,
  -19455, -19199, -18943, -18687,
  -18431, -18175, -17919, -17663,
  -17407, -17151, -16895, -16639,
  -16384, -16128, -15872, -15616,
  -15360, -15104, -14848, -14592,
  -14336, -14080, -13824, -13568,
  -13312, -13056, -12800, -12544,
  -12288, -12032, -11776, -11520,
  -11264, -11008, -10752, -10496,
  -10240,  -9984,  -9728,  -9472,
   -9216,  -8960,  -8704,  -8448,
   -8192,  -7936,  -7680,  -7424,
   -7168,  -6912,  -6656,  -6400,
   -6144,  -5888,  -5632,  -5376,
   -5120,  -4864,  -4608,  -4352,
   -4096,  -3840,  -3584,  -3328,
   -3072,  -2816,  -2560,  -2304,
   -2048,  -1792,  -1536,  -1280,
   -1024,   -768,   -512,   -256,
       0,    256,    512,    768,
    1024,   1280,   1536,   1792,
    2048,   2304,   2560,   2816,
    3072,   3328,   3584,   3840,
    4096,   4352,   4608,   4864,
    5120,   5376,   5632,   5888,
    6144,   6400,   6656,   6912,
    7168,   7424,   7680,   7936,
    8192,   8448,   8704,   8960,
    9216,   9472,   9728,   9984,
   10240,  10496,  10752,  11008,
   11264,  11520,  11776,  12032,
   12288,  12544,  12800,  13056,
   13312,  13568,  13824,  14080,
   14336,  14592,  14848,  15104,
   15360,  15616,  15872,  16128,
   16384,  16639,  16895,  17151,
   17407,  17663,  17919,  18175,
   18431,  18687,  18943,  19199,
   19455,  19711,  19967,  20223,
   20479,  20735,  20991,  21247,
   21503,  21759,  22015,  22271,
   22527,  22783,  23039,  23295,
   23551,  23807,  24063,  24319,
   24575,  24831,  25087,  25343,
   25599,  25855,  26111,  26367,
   26623,  26879,  27135,  27391,
   27647,  27903,  28159,  28415,
   28671,  28927,  29183,  29439,
   29695,  29951,  30207,  30463,
   30719,  30975,  31231,  31487,
   31743,  31999,  32255,  32511,
   32767,
};
const int16_t lut_ws_bump[] = {
       0,    -36,   -150,   -348,
    -636,  -1017,  -1496,  -2074,
   -2752,  -3528,  -4401,  -5366,
   -6417,  -7548,  -8750, -10013,
  -11327, -12679, -14056, -15444,
  -16829, -18197, -19530, -20816,
  -22039, -23185, -24239, -25190,
  -26025, -26733, -27306, -27736,
  -28018, -28214, -28391, -28550,
  -28690, -28810, -28912, -28994,
  -29056, -29099, -29122, -29125,
  -29109, -29073, -29017, -28941,
  -28846, -28732, -28599, -28446,
  -28275, -28085, -27877, -27651,
  -27407, -27145, -26867, -26572,
  -26260, -25933, -25590, -25233,
  -24861, -24475, -24075, -23663,
  -23238, -22802, -22354, -21896,
  -21428, -20951, -20465, -19971,
  -19469, -18961, -18447, -17928,
  -17404, -16877, -16346, -15813,
  -15278, -14742, -14206, -13670,
  -13136, -12603, -12073, -11547,
  -11025, -10507,  -9995,  -9489,
   -8990,  -8499,  -8015,  -7541,
   -7076,  -6621,  -6178,  -5745,
   -5324,  -4916,  -4521,  -4140,
   -3773,  -3420,  -3082,  -2760,
   -2454,  -2165,  -1892,  -1636,
   -1398,  -1178,   -976,   -792,
    -627,   -481,   -354,   -246,
    -158,    -89,    -39,    -10,
       0,     10,     39,     89,
     158,    246,    354,    481,
     627,    792,    976,   1178,
    1398,   1636,   1892,   2165,
    2454,   2760,   3082,   3420,
    3773,   4140,   4521,   4916,
    5324,   5745,   6178,   6621,
    7076,   7541,   8015,   8499,
    8990,   9489,   9995,  10507,
   11025,  11547,  12073,  12603,
   13136,  13670,  14206,  14742,
   15278,  15813,  16346,  16877,
   17404,  17928,  18447,  18961,
   19469,  19971,  20465,  20951,
   21428,  21896,  22354,  22802,
   23238,  23663,  24075,  24475,
   24861,  25233,  25590,  25933,
   26260,  26572,  26867,  27145,
   27407,  27651,  27877,  28085,
   28275,  28446,  28599,  28732,
   28846,  28941,  29017,  29073,
   29109,  29125,  29122,  29099,
   29056,  28994,  28912,  28810,
   28690,  28550,  28391,  28214,
   28018,  27736,  27306,  26733,
   26025,  25190,  24239,  23185,
   22039,  20816,  19530,  18197,
   16829,  15444,  14056,  12679,
   11327,  10013,   8750,   7548,
    6417,   5366,   4401,   3528,
    2752,   2074,   1496,   1017,
     636,    348,    150,     36,
       0,
};
const int16_t lut_ws_double_bump[] = {
   32767,  32745,  32678,  32567,
   32412,  32213,  31971,  31685,
   31356,  30985,  30571,  30117,
   29621,  29085,  28510,  27896,
   27245,  26556,  25832,  25072,
   24279,  23452,  22594,  21705,
   20787,  19841,  18868,  17869,
   16846,  15800,  14732,  13645,
   12539,  11417,  10278,   9126,
    7962,   6786,   5602,   4410,
    3212,   2009,    804,   -402,
   -1608,  -2811,  -4011,  -5205,
   -6393,  -7571,  -8739,  -9896,
  -11039, -12167, -13279, -14372,
  -15446, -16499, -17530, -18537,
  -19519, -20475, -21403, -22301,
  -23170, -24007, -24811, -25582,
  -26319, -27019, -27683, -28310,
  -28898, -29447, -29956, -30424,
  -30852, -31237, -31580, -31880,
  -32137, -32351, -32521, -32646,
  -32728, -32765, -32757, -32705,
  -32609, -32469, -32285, -32057,
  -31785, -31470, -31113, -30714,
  -30273, -29791, -29268, -28706,
  -28105, -27466, -26790, -26077,
  -25329, -24547, -23731, -22884,
  -22005, -21096, -20159, -19195,
  -18204, -17189, -16151, -15090,
  -14010, -12910, -11793, -10659,
   -9512,  -8351,  -7179,  -5998,
   -4808,  -3612,  -2410,  -1206,
       0,   1206,   2410,   3612,
    4808,   5998,   7179,   8351,
    9512,  10659,  11793,  12910,
   14010,  15090,  16151,  17189,
   18204,  19195,  20159,  21096,
   22005,  22884,  23731,  24547,
   25329,  26077,  26790,  27466,
   28105,  28706,  29268,  29791,
   30273,  30714,  31113,  31470,
   31785,  32057,  32285,  32469,
   32609,  32705,  32757,  32765,
   32728,  32646,  32521,  32351,
   32137,  31880,  31580,  31237,
   30852,  30424,  29956,  29447,
   28898,  28310,  27683,  27019,
   26319,  25582,  24811,  24007,
   23170,  22301,  21403,  20475,
   19519,  18537,  17530,  16499,
   15446,  14372,  13279,  12167,
   11039,   9896,   8739,   7571,
    6393,   5205,   4011,   2811,
    1608,    402,   -804,  -2009,
   -3212,  -4410,  -5602,  -6786,
   -7962,  -9126, -10278, -11417,
  -12539, -13645, -14732, -15800,
  -16846, -17869, -18868, -19841,
  -20787, -21705, -22594, -23452,
  -24279, -25072, -25832, -26556,
  -27245, -27896, -28510, -29085,
  -29621, -30117, -30571, -30985,
  -31356, -31685, -31971, -32213,
  -32412, -32567, -32678, -32745,
  -32767,
};


const int16_t* lookup_table_i16_table[] = {
  lut_ws_inverse_tan,
  lut_ws_inverse_sin,
  lut_ws_linear,
  lut_ws_bump,
  lut_ws_double_bump,
  lut_ws_double_bump,
};

const int8_t lut_lpc_excitation_pulse[] = {
       0,      0,      0,      0,
       1,      1,      1,      2,
       3,      3,      4,      5,
       6,      7,      8,      9,
      10,     12,     13,     15,
      17,     19,     21,     23,
      25,     28,     30,     33,
      36,     38,     41,     44,
      48,     51,     54,     57,
      61,     64,     68,     71,
      75,     78,     82,     85,
      89,     92,     95,     99,
     102,    105,    108,    110,
     113,    115,    118,    120,
     121,    123,    124,    125,
     126,    127,    127,    127,
     127,    126,    125,    124,
     122,    121,    118,    116,
     113,    110,    107,    104,
     100,     96,     92,     87,
      83,     78,     73,     68,
      63,     58,     53,     47,
      42,     37,     31,     26,
      21,     16,     11,      6,
       1,     -3,     -8,    -12,
     -16,    -20,    -23,    -26,
     -29,    -32,    -35,    -37,
     -39,    -40,    -42,    -43,
     -43,    -44,    -44,    -44,
     -44,    -44,    -43,    -42,
     -41,    -40,    -39,    -38,
     -36,    -35,    -33,    -32,
     -30,    -29,    -27,    -26,
     -24,    -23,    -22,    -20,
     -19,    -18,    -18,    -17,
     -16,    -16,    -16,    -16,
     -16,    -16,    -17,    -17,
     -18,    -19,    -20,    -21,
     -23,    -24,    -26,    -27,
     -29,    -30,    -32,    -34,
     -35,    -37,    -39,    -40,
     -42,    -43,    -44,    -46,
     -47,    -48,    -48,    -49,
     -49,    -50,    -50,    -50,
     -49,    -49,    -48,    -47,
     -46,    -45,    -44,    -42,
     -41,    -39,    -37,    -35,
     -33,    -31,    -29,    -27,
     -25,    -23,    -20,    -18,
     -16,    -14,    -13,    -11,
      -9,     -8,     -7,     -6,
      -5,     -4,     -3,     -3,
      -3,     -3,     -3,     -4,
      -5,     -6,     -7,     -9,
     -10,    -12,    -14,    -16,
     -18,    -21,    -23,    -26,
     -29,    -32,    -34,    -37,
     -40,    -43,    -46,    -49,
     -51,    -54,    -56,    -59,
     -61,    -63,    -65,    -67,
     -68,    -70,    -71,    -72,
     -72,    -73,    -73,    -73,
     -73,    -72,    -72,    -71,
     -70,    -69,    -67,    -66,
     -64,    -63,    -61,    -59,
     -57,    -54,    -52,    -50,
     -48,    -45,    -43,    -41,
     -39,    -37,    -35,    -33,
     -31,    -29,    -27,    -26,
     -25,    -23,    -22,    -21,
     -20,    -20,    -19,    -19,
     -19,    -18,    -18,    -18,
     -19,    -19,    -19,    -20,
     -20,    -21,    -21,    -22,
     -22,    -23,    -23,    -24,
     -24,    -25,    -25,    -25,
     -26,    -26,    -26,    -25,
     -25,    -25,    -24,    -24,
     -23,    -22,    -21,    -20,
     -19,    -18,    -16,    -15,
     -13,    -12,    -10,     -8,
      -6,     -4,     -3,     -1,
       1,      3,      5,      7,
       8,     10,     12,     13,
      15,     16,     17,     18,
      19,     20,     21,     21,
      22,     22,     22,     22,
      22,     22,     22,     22,
      21,     21,     20,     19,
      19,     18,     17,     16,
      15,     14,     14,     13,
      12,     11,     10,     10,
       9,      9,      8,      8,
       8,      8,      8,      8,
       8,      8,      8,      9,
       9,     10,     11,     12,
      13,     14,     15,     16,
      17,     18,     19,     21,
      22,     23,     24,     26,
      27,     28,     29,     30,
      31,     32,     33,     33,
      34,     35,     35,     35,
      36,     36,     36,     36,
      35,     35,     35,     34,
      34,     33,     33,     32,
      31,     30,     30,     29,
      28,     27,     26,     25,
      25,     24,     23,     22,
      22,     21,     20,     20,
      19,     19,     19,     19,
      19,     19,     19,     19,
      19,     19,     20,     20,
      21,     21,     22,     22,
      23,     23,     24,     25,
      25,     26,     27,     27,
      28,     29,     29,     29,
      30,     30,     30,     31,
      31,     31,     31,     30,
      30,     30,     29,     29,
      28,     28,     27,     26,
      26,     25,     24,     23,
      22,     21,     20,     19,
      18,     17,     16,     15,
      15,     14,     13,     12,
      12,     11,     10,     10,
      10,      9,      9,      9,
       9,      9,      9,      9,
       9,     10,     10,     10,
      11,     11,     12,     12,
      12,     13,     13,     14,
      14,     14,     15,     15,
      15,     15,     15,     15,
      15,     15,     15,     15,
      14,     14,     14,     13,
      12,     12,     11,     10,
       9,      8,      8,      7,
       6,      5,      4,      3,
       2,      1,      0,     -1,
      -2,     -3,     -4,     -4,
      -5,     -6,     -6,     -7,
      -7,     -8,     -8,     -8,
      -9,     -9,     -9,     -9,
      -9,     -9,     -9,     -9,
      -8,     -8,     -8,     -7,
      -7,     -7,     -6,     -6,
      -5,     -5,     -5,     -4,
      -4,     -4,     -3,     -3,
      -3,     -2,     -2,     -2,
      -2,     -1,     -1,     -1,
      -1,     -1,     -1,     -1,
      -1,     -1,     -1,     -1,
      -1,     -1,     -2,     -2,
      -2,     -2,     -2,     -2,
      -2,     -2,     -2,     -2,
      -2,     -2,     -2,     -2,
      -2,     -2,     -2,     -2,
      -2,     -2,     -2,     -2,
      -2,     -1,     -1,     -1,
      -1,     -1,     -1,      0,
       0,      0,      0,      0,
};


const int8_t* lookup_table_i8_table[] = {
  lut_lpc_excitation_pulse,
};

const int16_t wav_integrated_waves[] = {
  -20784, -20822, -20847, -20860,
  -20860, -20847, -20822, -20784,
  -20734, -20671, -20596, -20509,
  -20409, -20297, -20172, -20036,
  -19887, -19727, -19554, -19370,
  -19174, -18966, -18747, -18517,
  -18276, -18024, -17760, -17486,
  -17202, -16907, -16602, -16287,
  -15962, -15628, -15284, -14931,
  -14569, -14198, -13819, -13431,
  -13035, -12632, -12220, -11802,
  -11376, -10944, -10504, -10059,
   -9607,  -9150,  -8687,  -8219,
   -7746,  -7268,  -6786,  -6300,
   -5810,  -5317,  -4820,  -4321,
   -3818,  -3314,  -2808,  -2299,
   -1790,  -1279,   -768,   -256,
     256,    768,   1279,   1790,
    2299,   2808,   3314,   3818,
    4321,   4820,   5317,   5810,
    6300,   6786,   7268,   7746,
    8219,   8687,   9150,   9607,
   10059,  10504,  10944,  11376,
   11802,  12220,  12632,  13035,
   13431,  13819,  14198,  14569,
   14931,  15284,  15628,  15962,
   16287,  16602,  16907,  17202,
   17486,  17760,  18024,  18276,
   18517,  18747,  18966,  19174,
   19370,  19554,  19727,  19887,
   20036,  20172,  20297,  20409,
   20509,  20596,  20671,  20734,
   20784,  20822,  20847,  20860,
   20860,  20847,  20822,  20784,
   20734,  20671,  20596,  20509,
   20409,  20297,  20172,  20036,
   19887,  19727,  19554,  19370,
   19174,  18966,  18747,  18517,
   18276,  18024,  17760,  17486,
   17202,  16907,  16602,  16287,
   15962,  15628,  15284,  14931,
   14569,  14198,  13819,  13431,
   13035,  12632,  12220,  11802,
   11376,  10944,  10504,  10059,
    9607,   9150,   8687,   8219,
    7746,   7268,   6786,   6300,
    5810,   5317,   4820,   4321,
    3818,   3314,   2808,   2299,
    1790,   1279,    768,    256,
    -256,   -768,  -1279,  -1790,
   -2299,  -2808,  -3314,  -3818,
   -4321,  -4820,  -5317,  -5810,
   -6300,  -6786,  -7268,  -7746,
   -8219,  -8687,  -9150,  -9607,
  -10059, -10504, -10944, -11376,
  -11802, -12220, -12632, -13035,
  -13431, -13819, -14198, -14569,
  -14931, -15284, -15628, -15962,
  -16287, -16602, -16907, -17202,
  -17486, -17760, -18024, -18276,
  -18517, -18747, -18966, -19174,
  -19370, -19554, -19727, -19887,
  -20036, -20172, -20297, -20409,
  -20509, -20596, -20671, -20734,
  -20784, -20822, -20847, -20860,
  -10278, -10353, -10403, -10428,
  -10428, -10403, -10353, -10278,
  -10178, -10054,  -9905,  -9732,
   -9537,  -9318,  -9076,  -8813,
   -8529,  -8224,  -7899,  -7555,
   -7193,  -6814,  -6418,  -6007,
   -5581,  -5142,  -4690,  -4227,
   -3754,  -3272,  -2782,  -2286,
   -1783,  -1277,   -767,   -256,
     256,    767,   1277,   1783,
    2286,   2782,   3272,   3754,
    4227,   4690,   5142,   5581,
    6007,   6418,   6814,   7193,
    7555,   7899,   8224,   8529,
    8813,   9076,   9318,   9537,
    9732,   9905,  10054,  10178,
   10278,  10353,  10403,  10428,
   10428,  10403,  10353,  10278,
   10178,  10054,   9905,   9732,
    9537,   9318,   9076,   8813,
    8529,   8224,   7899,   7555,
    7193,   6814,   6418,   6007,
    5581,   5142,   4690,   4227,
    3754,   3272,   2782,   2286,
    1783,   1277,    767,    256,
    -256,   -767,  -1277,  -1783,
   -2286,  -2782,  -3272,  -3754,
   -4227,  -4690,  -5142,  -5581,
   -6007,  -6418,  -6814,  -7193,
   -7555,  -7899,  -8224,  -8529,
   -8813,  -9076,  -9318,  -9537,
   -9732,  -9905, -10054, -10178,
  -10278, -10353, -10403, -10428,
  -10428, -10403, -10353, -10278,
  -10178, -10054,  -9905,  -9732,
   -9537,  -9318,  -9076,  -8813,
   -8529,  -8224,  -7899,  -7555,
   -7193,  -6814,  -6418,  -6007,
   -5581,  -5142,  -4690,  -4227,
   -3754,  -3272,  -2782,  -2286,
   -1783,  -1277,   -767,   -256,
     256,    767,   1277,   1783,
    2286,   2782,   3272,   3754,
    4227,   4690,   5142,   5581,
    6007,   6418,   6814,   7193,
    7555,   7899,   8224,   8529,
    8813,   9076,   9318,   9537,
    9732,   9905,  10054,  10178,
   10278,  10353,  10403,  10428,
   10428,  10403,  10353,  10278,
   10178,  10054,   9905,   9732,
    9537,   9318,   9076,   8813,
    8529,   8224,   7899,   7555,
    7193,   6814,   6418,   6007,
    5581,   5142,   4690,   4227,
    3754,   3272,   2782,   2286,
    1783,   1277,    767,    256,
    -256,   -767,  -1277,  -1783,
   -2286,  -2782,  -3272,  -3754,
   -4227,  -4690,  -5142,  -5581,
   -6007,  -6418,  -6814,  -7193,
   -7555,  -7899,  -8224,  -8529,
   -8813,  -9076,  -9318,  -9537,
   -9732,  -9905, -10054, -10178,
  -10278, -10353, -10403, -10428,
   -6725,  -6838,  -6913,  -6950,
   -6950,  -6913,  -6838,  -6725,
   -6577,  -6393,  -6174,  -5921,
   -5637,  -5322,  -4978,  -4607,
   -4211,  -3793,  -3354,  -2896,
   -2423,  -1937,  -1440,   -936,
    -426,     85,    597,   1105,
    1607,   2100,   2583,   3051,
    3502,   3935,   4346,   4734,
    5096,   5430,   5735,   6009,
    6250,   6458,   6630,   6767,
    6867,   6930,   6955,   6942,
    6892,   6804,   6680,   6519,
    6323,   6093,   5830,   5535,
    5210,   4857,   4478,   4074,
    3649,   3203,   2740,   2263,
    1773,   1273,    767,    256,
    -256,   -767,  -1273,  -1773,
   -2263,  -2740,  -3203,  -3649,
   -4074,  -4478,  -4857,  -5210,
   -5535,  -5830,  -6093,  -6323,
   -6519,  -6680,  -6804,  -6892,
   -6942,  -6955,  -6930,  -6867,
   -6767,  -6630,  -6458,  -6250,
   -6009,  -5735,  -5430,  -5096,
   -4734,  -4346,  -3935,  -3502,
   -3051,  -2583,  -2100,  -1607,
   -1105,   -597,    -85,    426,
     936,   1440,   1937,   2423,
    2896,   3354,   3793,   4211,
    4607,   4978,   5322,   5637,
    5921,   6174,   6393,   6577,
    6725,   6838,   6913,   6950,
    6950,   6913,   6838,   6725,
    6577,   6393,   6174,   5921,
    5637,   5322,   4978,   4607,
    4211,   3793,   3354,   2896,
    2423,   1937,   1440,    936,
     426,    -85,   -597,  -1105,
   -1607,  -2100,  -2583,  -3051,
   -3502,  -3935,  -4346,  -4734,
   -5096,  -5430,  -5735,  -6009,
   -6250,  -6458,  -6630,  -6767,
   -6867,  -6930,  -6955,  -6942,
   -6892,  -6804,  -6680,  -6519,
   -6323,  -6093,  -5830,  -5535,
   -5210,  -4857,  -4478,  -4074,
   -3649,  -3203,  -2740,  -2263,
   -1773,  -1273,   -767,   -256,
     256,    767,   1273,   1773,
    2263,   2740,   3203,   3649,
    4074,   4478,   4857,   5210,
    5535,   5830,   6093,   6323,
    6519,   6680,   6804,   6892,
    6942,   6955,   6930,   6867,
    6767,   6630,   6458,   6250,
    6009,   5735,   5430,   5096,
    4734,   4346,   3935,   3502,
    3051,   2583,   2100,   1607,
    1105,    597,     85,   -426,
    -936,  -1440,  -1937,  -2423,
   -2896,  -3354,  -3793,  -4211,
   -4607,  -4978,  -5322,  -5637,
   -5921,  -6174,  -6393,  -6577,
   -6725,  -6838,  -6913,  -6950,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -3796,  -3980,  -4104,  -4167,
   -4167,  -4104,  -3980,  -3796,
   -3554,  -3259,  -2916,  -2528,
   -2102,  -1645,  -1163,   -663,
    -154,    358,    865,   1358,
    1831,   2277,   2688,   3059,
    3383,   3657,   3876,   4037,
    4137,   4174,   4149,   4062,
    3913,   3706,   3442,   3127,
    2765,   2362,   1923,   1455,
     965,    460,    -51,   -562,
   -1064,  -1550,  -2013,  -2446,
   -2841,  -3194,  -3499,  -3752,
   -3948,  -4084,  -4159,  -4172,
   -4122,  -4010,  -3837,  -3607,
   -3322,  -2988,  -2609,  -2190,
   -1738,  -1261,   -764,   -256,
     256,    764,   1261,   1738,
    2190,   2609,   2988,   3322,
    3607,   3837,   4010,   4122,
    4172,   4159,   4084,   3948,
    3752,   3499,   3194,   2841,
    2446,   2013,   1550,   1064,
     562,     51,   -460,   -965,
   -1455,  -1923,  -2362,  -2765,
   -3127,  -3442,  -3706,  -3913,
   -4062,  -4149,  -4174,  -4137,
   -4037,  -3876,  -3657,  -3383,
   -3059,  -2688,  -2277,  -1831,
   -1358,   -865,   -358,    154,
     663,   1163,   1645,   2102,
    2528,   2916,   3259,   3554,
    3796,   3980,   4104,   4167,
    4167,   4104,   3980,   3796,
    3554,   3259,   2916,   2528,
    2102,   1645,   1163,    663,
     154,   -358,   -865,  -1358,
   -1831,  -2277,  -2688,  -3059,
   -3383,  -3657,  -3876,  -4037,
   -4137,  -4174,  -4149,  -4062,
   -3913,  -3706,  -3442,  -3127,
   -2765,  -2362,  -1923,  -1455,
    -965,   -460,     51,    562,
    1064,   1550,   2013,   2446,
    2841,   3194,   3499,   3752,
    3948,   4084,   4159,   4172,
    4122,   4010,   3837,   3607,
    3322,   2988,   2609,   2190,
    1738,   1261,    764,    256,
    -256,   -764,  -1261,  -1738,
   -2190,  -2609,  -2988,  -3322,
   -3607,  -3837,  -4010,  -4122,
   -4172,  -4159,  -4084,  -3948,
   -3752,  -3499,  -3194,  -2841,
   -2446,  -2013,  -1550,  -1064,
    -562,    -51,    460,    965,
    1455,   1923,   2362,   2765,
    3127,   3442,   3706,   3913,
    4062,   4149,   4174,   4137,
    4037,   3876,   3657,   3383,
    3059,   2688,   2277,   1831,
    1358,    865,    358,   -154,
    -663,  -1163,  -1645,  -2102,
   -2528,  -2916,  -3259,  -3554,
   -3796,  -3980,  -4104,  -4167,
   -3028,  -3247,  -3395,  -3471,
   -3471,  -3395,  -3247,  -3028,
   -2743,  -2400,  -2004,  -1565,
   -1092,   -595,    -85,    426,
     928,   1410,   1862,   2273,
    2635,   2940,   3181,   3354,
    3454,   3479,   3429,   3304,
    3108,   2845,   2520,   2141,
    1715,   1252,    762,    256,
    -256,   -762,  -1252,  -1715,
   -2141,  -2520,  -2845,  -3108,
   -3304,  -3429,  -3479,  -3454,
   -3354,  -3181,  -2940,  -2635,
   -2273,  -1862,  -1410,   -928,
    -426,     85,    595,   1092,
    1565,   2004,   2400,   2743,
    3028,   3247,   3395,   3471,
    3471,   3395,   3247,   3028,
    2743,   2400,   2004,   1565,
    1092,    595,     85,   -426,
    -928,  -1410,  -1862,  -2273,
   -2635,  -2940,  -3181,  -3354,
   -3454,  -3479,  -3429,  -3304,
   -3108,  -2845,  -2520,  -2141,
   -1715,  -1252,   -762,   -256,
     256,    762,   1252,   1715,
    2141,   2520,   2845,   3108,
    3304,   3429,   3479,   3454,
    3354,   3181,   2940,   2635,
    2273,   1862,   1410,    928,
     426,    -85,   -595,  -1092,
   -1565,  -2004,  -2400,  -2743,
   -3028,  -3247,  -3395,  -3471,
   -3471,  -3395,  -3247,  -3028,
   -2743,  -2400,  -2004,  -1565,
   -1092,   -595,    -85,    426,
     928,   1410,   1862,   2273,
    2635,   2940,   3181,   3354,
    3454,   3479,   3429,   3304,
    3108,   2845,   2520,   2141,
    1715,   1252,    762,    256,
    -256,   -762,  -1252,  -1715,
   -2141,  -2520,  -2845,  -3108,
   -3304,  -3429,  -3479,  -3454,
   -3354,  -3181,  -2940,  -2635,
   -2273,  -1862,  -1410,   -928,
    -426,     85,    595,   1092,
    1565,   2004,   2400,   2743,
    3028,   3247,   3395,   3471,
    3471,   3395,   3247,   3028,
    2743,   2400,   2004,   1565,
    1092,    595,     85,   -426,
    -928,  -1410,  -1862,  -2273,
   -2635,  -2940,  -3181,  -3354,
   -3454,  -3479,  -3429,  -3304,
   -3108,  -2845,  -2520,  -2141,
   -1715,  -1252,   -762,   -256,
     256,    762,   1252,   1715,
    2141,   2520,   2845,   3108,
    3304,   3429,   3479,   3454,
    3354,   3181,   2940,   2635,
    2273,   1862,   1410,    928,
     426,    -85,   -595,  -1092,
   -1565,  -2004,  -2400,  -2743,
   -3028,  -3247,  -3395,  -3471,
   -2460,  -2713,  -2885,  -2973,
   -2973,  -2885,  -2713,  -2460,
   -2136,  -1748,  -1309,   -831,
    -329,    183,    689,   1176,
    1627,   2031,   2375,   2649,
    2844,   2957,   2982,   2919,
    2770,   2540,   2235,   1864,
    1439,    971,    474,    -37,
    -546,  -1040,  -1502,  -1921,
   -2283,  -2578,  -2797,  -2933,
   -2984,  -2946,  -2821,  -2614,
   -2330,  -1977,  -1565,  -1108,
    -618,   -110,    402,    901,
    1374,   1807,   2186,   2501,
    2742,   2903,   2978,   2966,
    2866,   2681,   2418,   2084,
    1688,   1243,    760,    256,
    -256,   -760,  -1243,  -1688,
   -2084,  -2418,  -2681,  -2866,
   -2966,  -2978,  -2903,  -2742,
   -2501,  -2186,  -1807,  -1374,
    -901,   -402,    110,    618,
    1108,   1565,   1977,   2330,
    2614,   2821,   2946,   2984,
    2933,   2797,   2578,   2283,
    1921,   1502,   1040,    546,
      37,   -474,   -971,  -1439,
   -1864,  -2235,  -2540,  -2770,
   -2919,  -2982,  -2957,  -2844,
   -2649,  -2375,  -2031,  -1627,
   -1176,   -689,   -183,    329,
     831,   1309,   1748,   2136,
    2460,   2713,   2885,   2973,
    2973,   2885,   2713,   2460,
    2136,   1748,   1309,    831,
     329,   -183,   -689,  -1176,
   -1627,  -2031,  -2375,  -2649,
   -2844,  -2957,  -2982,  -2919,
   -2770,  -2540,  -2235,  -1864,
   -1439,   -971,   -474,     37,
     546,   1040,   1502,   1921,
    2283,   2578,   2797,   2933,
    2984,   2946,   2821,   2614,
    2330,   1977,   1565,   1108,
     618,    110,   -402,   -901,
   -1374,  -1807,  -2186,  -2501,
   -2742,  -2903,  -2978,  -2966,
   -2866,  -2681,  -2418,  -2084,
   -1688,  -1243,   -760,   -256,
     256,    760,   1243,   1688,
    2084,   2418,   2681,   2866,
    2966,   2978,   2903,   2742,
    2501,   2186,   1807,   1374,
     901,    402,   -110,   -618,
   -1108,  -1565,  -1977,  -2330,
   -2614,  -2821,  -2946,  -2984,
   -2933,  -2797,  -2578,  -2283,
   -1921,  -1502,  -1040,   -546,
     -37,    474,    971,   1439,
    1864,   2235,   2540,   2770,
    2919,   2982,   2957,   2844,
    2649,   2375,   2031,   1627,
    1176,    689,    183,   -329,
    -831,  -1309,  -1748,  -2136,
   -2460,  -2713,  -2885,  -2973,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
  -10278, -10353, -10403, -10428,
  -10428, -10403, -10353, -10278,
  -10178, -10054,  -9905,  -9732,
   -9537,  -9318,  -9076,  -8813,
   -8529,  -8224,  -7899,  -7555,
   -7193,  -6814,  -6418,  -6007,
   -5581,  -5142,  -4690,  -4227,
   -3754,  -3272,  -2782,  -2286,
   -1783,  -1277,   -767,   -256,
     256,    767,   1277,   1783,
    2286,   2782,   3272,   3754,
    4227,   4690,   5142,   5581,
    6007,   6418,   6814,   7193,
    7555,   7899,   8224,   8529,
    8813,   9076,   9318,   9537,
    9732,   9905,  10054,  10178,
   10278,  10353,  10403,  10428,
   10428,  10403,  10353,  10278,
   10178,  10054,   9905,   9732,
    9537,   9318,   9076,   8813,
    8529,   8224,   7899,   7555,
    7193,   6814,   6418,   6007,
    5581,   5142,   4690,   4227,
    3754,   3272,   2782,   2286,
    1783,   1277,    767,    256,
    -256,   -767,  -1277,  -1783,
   -2286,  -2782,  -3272,  -3754,
   -4227,  -4690,  -5142,  -5581,
   -6007,  -6418,  -6814,  -7193,
   -7555,  -7899,  -8224,  -8529,
   -8813,  -9076,  -9318,  -9537,
   -9732,  -9905, -10054, -10178,
  -10278, -10353, -10403, -10428,
  -10428, -10403, -10353, -10278,
  -10178, -10054,  -9905,  -9732,
   -9537,  -9318,  -9076,  -8813,
   -8529,  -8224,  -7899,  -7555,
   -7193,  -6814,  -6418,  -6007,
   -5581,  -5142,  -4690,  -4227,
   -3754,  -3272,  -2782,  -2286,
   -1783,  -1277,   -767,   -256,
     256,    767,   1277,   1783,
    2286,   2782,   3272,   3754,
    4227,   4690,   5142,   5581,
    6007,   6418,   6814,   7193,
    7555,   7899,   8224,   8529,
    8813,   9076,   9318,   9537,
    9732,   9905,  10054,  10178,
   10278,  10353,  10403,  10428,
   10428,  10403,  10353,  10278,
   10178,  10054,   9905,   9732,
    9537,   9318,   9076,   8813,
    8529,   8224,   7899,   7555,
    7193,   6814,   6418,   6007,
    5581,   5142,   4690,   4227,
    3754,   3272,   2782,   2286,
    1783,   1277,    767,    256,
    -256,   -767,  -1277,  -1783,
   -2286,  -2782,  -3272,  -3754,
   -4227,  -4690,  -5142,  -5581,
   -6007,  -6418,  -6814,  -7193,
   -7555,  -7899,  -8224,  -8529,
   -8813,  -9076,  -9318,  -9537,
   -9732,  -9905, -10054, -10178,
  -10278, -10353, -10403, -10428,
   -6725,  -6838,  -6913,  -6950,
   -6950,  -6913,  -6838,  -6725,
   -6577,  -6393,  -6174,  -5921,
   -5637,  -5322,  -4978,  -4607,
   -4211,  -3793,  -3354,  -2896,
   -2423,  -1937,  -1440,   -936,
    -426,     85,    597,   1105,
    1607,   2100,   2583,   3051,
    3502,   3935,   4346,   4734,
    5096,   5430,   5735,   6009,
    6250,   6458,   6630,   6767,
    6867,   6930,   6955,   6942,
    6892,   6804,   6680,   6519,
    6323,   6093,   5830,   5535,
    5210,   4857,   4478,   4074,
    3649,   3203,   2740,   2263,
    1773,   1273,    767,    256,
    -256,   -767,  -1273,  -1773,
   -2263,  -2740,  -3203,  -3649,
   -4074,  -4478,  -4857,  -5210,
   -5535,  -5830,  -6093,  -6323,
   -6519,  -6680,  -6804,  -6892,
   -6942,  -6955,  -6930,  -6867,
   -6767,  -6630,  -6458,  -6250,
   -6009,  -5735,  -5430,  -5096,
   -4734,  -4346,  -3935,  -3502,
   -3051,  -2583,  -2100,  -1607,
   -1105,   -597,    -85,    426,
     936,   1440,   1937,   2423,
    2896,   3354,   3793,   4211,
    4607,   4978,   5322,   5637,
    5921,   6174,   6393,   6577,
    6725,   6838,   6913,   6950,
    6950,   6913,   6838,   6725,
    6577,   6393,   6174,   5921,
    5637,   5322,   4978,   4607,
    4211,   3793,   3354,   2896,
    2423,   1937,   1440,    936,
     426,    -85,   -597,  -1105,
   -1607,  -2100,  -2583,  -3051,
   -3502,  -3935,  -4346,  -4734,
   -5096,  -5430,  -5735,  -6009,
   -6250,  -6458,  -6630,  -6767,
   -6867,  -6930,  -6955,  -6942,
   -6892,  -6804,  -6680,  -6519,
   -6323,  -6093,  -5830,  -5535,
   -5210,  -4857,  -4478,  -4074,
   -3649,  -3203,  -2740,  -2263,
   -1773,  -1273,   -767,   -256,
     256,    767,   1273,   1773,
    2263,   2740,   3203,   3649,
    4074,   4478,   4857,   5210,
    5535,   5830,   6093,   6323,
    6519,   6680,   6804,   6892,
    6942,   6955,   6930,   6867,
    6767,   6630,   6458,   6250,
    6009,   5735,   5430,   5096,
    4734,   4346,   3935,   3502,
    3051,   2583,   2100,   1607,
    1105,    597,     85,   -426,
    -936,  -1440,  -1937,  -2423,
   -2896,  -3354,  -3793,  -4211,
   -4607,  -4978,  -5322,  -5637,
   -5921,  -6174,  -6393,  -6577,
   -6725,  -6838,  -6913,  -6950,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -5211,  -5161,  -5061,  -4912,
   -4716,  -4475,  -4191,  -3866,
   -3504,  -3108,  -2682,  -2231,
   -1758,  -1268,   -766,   -256,
     256,    766,   1268,   1758,
    2231,   2682,   3108,   3504,
    3866,   4191,   4475,   4716,
    4912,   5061,   5161,   5211,
    5211,   5161,   5061,   4912,
    4716,   4475,   4191,   3866,
    3504,   3108,   2682,   2231,
    1758,   1268,    766,    256,
    -256,   -766,  -1268,  -1758,
   -2231,  -2682,  -3108,  -3504,
   -3866,  -4191,  -4475,  -4716,
   -4912,  -5061,  -5161,  -5211,
   -3028,  -3247,  -3395,  -3471,
   -3471,  -3395,  -3247,  -3028,
   -2743,  -2400,  -2004,  -1565,
   -1092,   -595,    -85,    426,
     928,   1410,   1862,   2273,
    2635,   2940,   3181,   3354,
    3454,   3479,   3429,   3304,
    3108,   2845,   2520,   2141,
    1715,   1252,    762,    256,
    -256,   -762,  -1252,  -1715,
   -2141,  -2520,  -2845,  -3108,
   -3304,  -3429,  -3479,  -3454,
   -3354,  -3181,  -2940,  -2635,
   -2273,  -1862,  -1410,   -928,
    -426,     85,    595,   1092,
    1565,   2004,   2400,   2743,
    3028,   3247,   3395,   3471,
    3471,   3395,   3247,   3028,
    2743,   2400,   2004,   1565,
    1092,    595,     85,   -426,
    -928,  -1410,  -1862,  -2273,
   -2635,  -2940,  -3181,  -3354,
   -3454,  -3479,  -3429,  -3304,
   -3108,  -2845,  -2520,  -2141,
   -1715,  -1252,   -762,   -256,
     256,    762,   1252,   1715,
    2141,   2520,   2845,   3108,
    3304,   3429,   3479,   3454,
    3354,   3181,   2940,   2635,
    2273,   1862,   1410,    928,
     426,    -85,   -595,  -1092,
   -1565,  -2004,  -2400,  -2743,
   -3028,  -3247,  -3395,  -3471,
   -3471,  -3395,  -3247,  -3028,
   -2743,  -2400,  -2004,  -1565,
   -1092,   -595,    -85,    426,
     928,   1410,   1862,   2273,
    2635,   2940,   3181,   3354,
    3454,   3479,   3429,   3304,
    3108,   2845,   2520,   2141,
    1715,   1252,    762,    256,
    -256,   -762,  -1252,  -1715,
   -2141,  -2520,  -2845,  -3108,
   -3304,  -3429,  -3479,  -3454,
   -3354,  -3181,  -2940,  -2635,
   -2273,  -1862,  -1410,   -928,
    -426,     85,    595,   1092,
    1565,   2004,   2400,   2743,
    3028,   3247,   3395,   3471,
    3471,   3395,   3247,   3028,
    2743,   2400,   2004,   1565,
    1092,    595,     85,   -426,
    -928,  -1410,  -1862,  -2273,
   -2635,  -2940,  -3181,  -3354,
   -3454,  -3479,  -3429,  -3304,
   -3108,  -2845,  -2520,  -2141,
   -1715,  -1252,   -762,   -256,
     256,    762,   1252,   1715,
    2141,   2520,   2845,   3108,
    3304,   3429,   3479,   3454,
    3354,   3181,   2940,   2635,
    2273,   1862,   1410,    928,
     426,    -85,   -595,  -1092,
   -1565,  -2004,  -2400,  -2743,
   -3028,  -3247,  -3395,  -3471,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
    -256,   -758,  -1231,  -1657,
   -2019,  -2303,  -2499,  -2599,
   -2599,  -2499,  -2303,  -2019,
   -1657,  -1231,   -758,   -256,
     256,    758,   1231,   1657,
    2019,   2303,   2499,   2599,
    2599,   2499,   2303,   2019,
    1657,   1231,    758,    256,
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     591,    703,    801,    883,
     950,   1000,   1036,   1057,
    1066,   1065,   1056,   1043,
    1027,   1011,    999,    991,
     991,   1000,   1019,   1049,
    1089,   1140,   1201,   1270,
    1346,   1427,   1510,   1594,
    1676,   1755,   1827,   1892,
    1948,   1993,   2028,   2052,
    2065,   2068,   2062,   2049,
    2030,   2006,   1981,   1955,
    1931,   1911,   1897,   1889,
    1889,   1897,   1915,   1940,
    1974,   2015,   2062,   2114,
    2168,   2223,   2278,   2330,
    2377,   2418,   2452,   2478,
    2494,   2501,   2499,   2489,
    2470,   2444,   2412,   2377,
    2339,   2301,   2265,   2231,
    2203,   2180,   2164,   2156,
    2156,   2164,   2180,   2203,
    2231,   2265,   2301,   2339,
    2377,   2412,   2444,   2470,
    2489,   2499,   2501,   2494,
    2478,   2452,   2418,   2377,
    2330,   2278,   2223,   2168,
    2114,   2062,   2015,   1974,
    1940,   1915,   1897,   1889,
    1889,   1897,   1911,   1931,
    1955,   1981,   2006,   2030,
    2049,   2062,   2068,   2065,
    2052,   2028,   1993,   1948,
    1892,   1827,   1755,   1676,
    1594,   1510,   1427,   1346,
    1270,   1201,   1140,   1089,
    1049,   1019,   1000,    991,
     991,    999,   1011,   1027,
    1043,   1056,   1065,   1066,
    1057,   1036,   1000,    950,
     883,    801,    703,    591,
     466,    331,    188,     41,
    -107,   -253,   -393,   -524,
    -644,   -749,   -839,   -912,
    -967,  -1005,  -1029,  -1039,
   -1039,  -1032,  -1025,  -1020,
   -1025,  -1044,  -1084,  -1149,
   -1244,  -1375,  -1545,  -1756,
   -2011,  -2309,  -2650,  -3032,
   -3451,  -3903,  -4381,  -4878,
   -5387,  -5899,  -6405,  -6895,
   -7360,  -7790,  -8178,  -8514,
   -8792,  -9006,  -9151,  -9224,
   -6114,  -6437,  -6663,  -6779,
   -6779,  -6663,  -6437,  -6114,
   -5710,  -5247,  -4748,  -4236,
   -3734,  -3263,  -2840,  -2477,
   -2180,  -1953,  -1790,  -1686,
   -1629,  -1606,  -1603,  -1606,
   -1603,  -1584,  -1542,  -1473,
   -1378,  -1259,  -1122,   -974,
    -824,   -680,   -549,   -436,
    -347,   -282,   -240,   -218,
    -212,   -215,   -222,   -224,
    -218,   -199,   -165,   -114,
     -49,     29,    114,    202,
     287,    365,    432,    485,
     523,    545,    554,    553,
     545,    536,    529,    528,
     537,    557,    589,    633,
     685,    743,    804,    864,
     918,    963,    998,   1022,
    1033,   1035,   1028,   1016,
    1003,    992,    986,    988,
    1000,   1021,   1051,   1090,
    1133,   1178,   1222,   1262,
    1295,   1319,   1333,   1337,
    1332,   1320,   1304,   1287,
    1272,   1261,   1257,   1262,
    1275,   1297,   1326,   1359,
    1394,   1428,   1459,   1482,
    1498,   1505,   1502,   1491,
    1474,   1454,   1432,   1411,
    1396,   1387,   1385,   1392,
    1407,   1429,   1455,   1483,
    1509,   1532,   1549,   1558,
    1558,   1549,   1532,   1509,
    1483,   1455,   1429,   1407,
    1392,   1385,   1387,   1396,
    1411,   1432,   1454,   1474,
    1491,   1502,   1505,   1498,
    1482,   1459,   1428,   1394,
    1359,   1326,   1297,   1275,
    1262,   1257,   1261,   1272,
    1287,   1304,   1320,   1332,
    1337,   1333,   1319,   1295,
    1262,   1222,   1178,   1133,
    1090,   1051,   1021,   1000,
     988,    986,    992,   1003,
    1016,   1028,   1035,   1033,
    1022,    998,    963,    918,
     864,    804,    743,    685,
     633,    589,    557,    537,
     528,    529,    536,    545,
     553,    554,    545,    523,
     485,    432,    365,    287,
     202,    114,     29,    -49,
    -114,   -165,   -199,   -218,
    -224,   -222,   -215,   -212,
    -218,   -240,   -282,   -347,
    -436,   -549,   -680,   -824,
    -974,  -1122,  -1259,  -1378,
   -1473,  -1542,  -1584,  -1603,
   -1606,  -1603,  -1606,  -1629,
   -1686,  -1790,  -1953,  -2180,
   -2477,  -2840,  -3263,  -3734,
   -4236,  -4748,  -5247,  -5710,
   -6114,  -6437,  -6663,  -6779,
   -3934,  -4390,  -4733,  -4917,
   -4917,  -4733,  -4390,  -3934,
   -3422,  -2914,  -2463,  -2106,
   -1857,  -1713,  -1651,  -1638,
   -1639,  -1624,  -1572,  -1477,
   -1346,  -1196,  -1046,   -917,
    -822,   -764,   -740,   -737,
    -739,   -731,   -702,   -649,
    -573,   -484,   -395,   -318,
    -262,   -229,   -216,   -217,
    -220,   -216,   -196,   -159,
    -105,    -43,     20,     74,
     112,    133,    139,    136,
     132,    134,    148,    177,
     218,    266,    314,    354,
     382,    396,    397,    392,
     386,    387,    398,    421,
     454,    493,    531,    562,
     582,    591,    589,    582,
     575,    574,    582,    601,
     629,    661,    692,    717,
     732,    736,    732,    723,
     715,    712,    718,    734,
     757,    784,    810,    830,
     840,    841,    834,    823,
     814,    809,    814,    827,
     847,    870,    891,    907,
     914,    911,    902,    889,
     878,    872,    874,    885,
     903,    923,    941,    953,
     956,    950,    938,    923,
     910,    903,    904,    913,
     928,    945,    960,    969,
     969,    960,    945,    928,
     913,    904,    903,    910,
     923,    938,    950,    956,
     953,    941,    923,    903,
     885,    874,    872,    878,
     889,    902,    911,    914,
     907,    891,    870,    847,
     827,    814,    809,    814,
     823,    834,    841,    840,
     830,    810,    784,    757,
     734,    718,    712,    715,
     723,    732,    736,    732,
     717,    692,    661,    629,
     601,    582,    574,    575,
     582,    589,    591,    582,
     562,    531,    493,    454,
     421,    398,    387,    386,
     392,    397,    396,    382,
     354,    314,    266,    218,
     177,    148,    134,    132,
     136,    139,    133,    112,
      74,     20,    -43,   -105,
    -159,   -196,   -216,   -220,
    -217,   -216,   -229,   -262,
    -318,   -395,   -484,   -573,
    -649,   -702,   -731,   -739,
    -737,   -740,   -764,   -822,
    -917,  -1046,  -1196,  -1346,
   -1477,  -1572,  -1624,  -1639,
   -1638,  -1651,  -1713,  -1857,
   -2106,  -2463,  -2914,  -3422,
   -3934,  -4390,  -4733,  -4917,
   -2173,  -2685,  -3158,  -3442,
   -3442,  -3158,  -2685,  -2173,
   -1759,  -1513,  -1424,  -1416,
   -1405,  -1333,  -1201,  -1048,
    -926,   -863,   -849,   -850,
    -827,   -766,   -677,   -592,
    -537,   -517,   -518,   -512,
    -482,   -426,   -361,   -311,
    -287,   -284,   -285,   -271,
    -236,   -187,   -141,   -114,
    -106,   -108,   -104,    -84,
     -47,     -8,     22,     34,
      33,     32,     42,     67,
     101,    131,    147,    149,
     145,    148,    164,    191,
     219,    238,    244,    241,
     239,    247,    267,    293,
     313,    323,    321,    317,
     319,    332,    354,    375,
     387,    388,    384,    381,
     388,    405,    425,    439,
     444,    440,    435,    437,
     448,    465,    481,    489,
     487,    481,    478,    484,
     498,    514,    524,    525,
     519,    513,    514,    524,
     538,    550,    554,    549,
     542,    538,    544,    556,
     568,    575,    572,    564,
     557,    558,    567,    579,
     587,    588,    580,    571,
     567,    572,    582,    592,
     595,    590,    580,    572,
     572,    580,    590,    595,
     592,    582,    572,    567,
     571,    580,    588,    587,
     579,    567,    558,    557,
     564,    572,    575,    568,
     556,    544,    538,    542,
     549,    554,    550,    538,
     524,    514,    513,    519,
     525,    524,    514,    498,
     484,    478,    481,    487,
     489,    481,    465,    448,
     437,    435,    440,    444,
     439,    425,    405,    388,
     381,    384,    388,    387,
     375,    354,    332,    319,
     317,    321,    323,    313,
     293,    267,    247,    239,
     241,    244,    238,    219,
     191,    164,    148,    145,
     149,    147,    131,    101,
      67,     42,     32,     33,
      34,     22,     -8,    -47,
     -84,   -104,   -108,   -106,
    -114,   -141,   -187,   -236,
    -271,   -285,   -284,   -287,
    -311,   -361,   -426,   -482,
    -512,   -518,   -517,   -537,
    -592,   -677,   -766,   -827,
    -850,   -849,   -863,   -926,
   -1048,  -1201,  -1333,  -1405,
   -1416,  -1424,  -1513,  -1759,
   -2173,  -2685,  -3158,  -3442,
   -1197,  -1479,  -1991,  -2415,
   -2415,  -1991,  -1479,  -1197,
   -1153,  -1138,  -1021,   -869,
    -796,   -794,   -767,   -682,
    -602,   -578,   -578,   -542,
    -476,   -432,   -428,   -421,
    -381,   -332,   -311,   -312,
    -297,   -257,   -223,   -216,
    -216,   -194,   -158,   -139,
    -139,   -133,   -107,    -79,
     -70,    -72,    -60,    -33,
     -15,    -13,    -12,      5,
      28,     38,     37,     42,
      62,     80,     83,     82,
      92,    112,    123,    122,
     123,    137,    154,    159,
     156,    162,    178,    189,
     189,    188,    198,    213,
     219,    216,    218,    230,
     242,    244,    241,    246,
     259,    267,    265,    264,
     272,    284,    287,    283,
     285,    296,    304,    303,
     300,    305,    316,    320,
     316,    316,    324,    333,
     333,    328,    331,    340,
     345,    342,    339,    344,
     353,    354,    349,    349,
     356,    362,    360,    355,
     358,    366,    368,    363,
     360,    365,    372,    371,
     365,    365,    371,    375,
     371,    366,    368,    375,
     375,    368,    366,    371,
     375,    371,    365,    365,
     371,    372,    365,    360,
     363,    368,    366,    358,
     355,    360,    362,    356,
     349,    349,    354,    353,
     344,    339,    342,    345,
     340,    331,    328,    333,
     333,    324,    316,    316,
     320,    316,    305,    300,
     303,    304,    296,    285,
     283,    287,    284,    272,
     264,    265,    267,    259,
     246,    241,    244,    242,
     230,    218,    216,    219,
     213,    198,    188,    189,
     189,    178,    162,    156,
     159,    154,    137,    123,
     122,    123,    112,     92,
      82,     83,     80,     62,
      42,     37,     38,     28,
       5,    -12,    -13,    -15,
     -33,    -60,    -72,    -70,
     -79,   -107,   -133,   -139,
    -139,   -158,   -194,   -216,
    -216,   -223,   -257,   -297,
    -312,   -311,   -332,   -381,
    -421,   -428,   -432,   -476,
    -542,   -578,   -578,   -602,
    -682,   -767,   -794,   -796,
    -869,  -1021,  -1138,  -1153,
   -1197,  -1479,  -1991,  -2415,
  -11906, -12065, -12173, -12228,
  -12228, -12173, -12065, -11906,
  -11699, -11450, -11164, -10847,
  -10505, -10147,  -9778,  -9404,
   -9033,  -8669,  -8316,  -7978,
   -7657,  -7355,  -7071,  -6803,
   -6551,  -6309,  -6076,  -5845,
   -5612,  -5372,  -5120,  -4852,
   -4563,  -4250,  -3910,  -3543,
   -3147,  -2724,  -2275,  -1804,
   -1315,   -812,   -301,    211,
     718,   1213,   1691,   2144,
    2569,   2959,   3312,   3625,
    3897,   4127,   4317,   4469,
    4587,   4674,   4736,   4779,
    4808,   4831,   4852,   4877,
    4912,   4961,   5027,   5113,
    5220,   5348,   5494,   5658,
    5836,   6022,   6212,   6401,
    6581,   6746,   6891,   7010,
    7096,   7147,   7158,   7127,
    7052,   6935,   6775,   6575,
    6339,   6071,   5776,   5461,
    5132,   4794,   4455,   4121,
    3797,   3487,   3197,   2928,
    2683,   2463,   2267,   2093,
    1940,   1803,   1678,   1561,
    1447,   1330,   1206,   1070,
     918,    747,    554,    338,
      99,   -162,   -443,   -740,
   -1049,  -1366,  -1683,  -1995,
   -2295,  -2575,  -2830,  -3053,
   -3239,  -3382,  -3480,  -3530,
   -3530,  -3480,  -3382,  -3239,
   -3053,  -2830,  -2575,  -2295,
   -1995,  -1683,  -1366,  -1049,
    -740,   -443,   -162,     99,
     338,    554,    747,    918,
    1070,   1206,   1330,   1447,
    1561,   1678,   1803,   1940,
    2093,   2267,   2463,   2683,
    2928,   3197,   3487,   3797,
    4121,   4455,   4794,   5132,
    5461,   5776,   6071,   6339,
    6575,   6775,   6935,   7052,
    7127,   7158,   7147,   7096,
    7010,   6891,   6746,   6581,
    6401,   6212,   6022,   5836,
    5658,   5494,   5348,   5220,
    5113,   5027,   4961,   4912,
    4877,   4852,   4831,   4808,
    4779,   4736,   4674,   4587,
    4469,   4317,   4127,   3897,
    3625,   3312,   2959,   2569,
    2144,   1691,   1213,    718,
     211,   -301,   -812,  -1315,
   -1804,  -2275,  -2724,  -3147,
   -3543,  -3910,  -4250,  -4563,
   -4852,  -5120,  -5372,  -5612,
   -5845,  -6076,  -6309,  -6551,
   -6803,  -7071,  -7355,  -7657,
   -7978,  -8316,  -8669,  -9033,
   -9404,  -9778, -10147, -10505,
  -10847, -11164, -11450, -11699,
  -11906, -12065, -12173, -12228,
   -7811,  -8116,  -8333,  -8447,
   -8447,  -8333,  -8116,  -7811,
   -7440,  -7030,  -6605,  -6187,
   -5791,  -5427,  -5094,  -4788,
   -4497,  -4204,  -3895,  -3557,
   -3179,  -2758,  -2297,  -1805,
   -1295,   -783,   -286,    184,
     614,   1000,   1341,   1641,
    1910,   2156,   2389,   2616,
    2842,   3065,   3281,   3479,
    3649,   3779,   3860,   3886,
    3855,   3772,   3645,   3488,
    3316,   3143,   2982,   2840,
    2719,   2616,   2519,   2415,
    2288,   2122,   1905,   1631,
    1300,    922,    512,     93,
    -311,   -673,   -971,  -1187,
   -1312,  -1344,  -1292,  -1172,
   -1005,   -815,   -625,   -457,
    -324,   -235,   -189,   -178,
    -189,   -205,   -210,   -188,
    -129,    -28,    113,    289,
     485,    689,    885,   1059,
    1202,   1311,   1385,   1430,
    1455,   1471,   1488,   1513,
    1552,   1604,   1663,   1721,
    1767,   1790,   1780,   1731,
    1641,   1514,   1360,   1190,
    1020,    863,    732,    633,
     566,    529,    508,    490,
     458,    394,    287,    128,
     -83,   -337,   -619,   -910,
   -1183,  -1416,  -1584,  -1673,
   -1673,  -1584,  -1416,  -1183,
    -910,   -619,   -337,    -83,
     128,    287,    394,    458,
     490,    508,    529,    566,
     633,    732,    863,   1020,
    1190,   1360,   1514,   1641,
    1731,   1780,   1790,   1767,
    1721,   1663,   1604,   1552,
    1513,   1488,   1471,   1455,
    1430,   1385,   1311,   1202,
    1059,    885,    689,    485,
     289,    113,    -28,   -129,
    -188,   -210,   -205,   -189,
    -178,   -189,   -235,   -324,
    -457,   -625,   -815,  -1005,
   -1172,  -1292,  -1344,  -1312,
   -1187,   -971,   -673,   -311,
      93,    512,    922,   1300,
    1631,   1905,   2122,   2288,
    2415,   2519,   2616,   2719,
    2840,   2982,   3143,   3316,
    3488,   3645,   3772,   3855,
    3886,   3860,   3779,   3649,
    3479,   3281,   3065,   2842,
    2616,   2389,   2156,   1910,
    1641,   1341,   1000,    614,
     184,   -286,   -783,  -1295,
   -1805,  -2297,  -2758,  -3179,
   -3557,  -3895,  -4204,  -4497,
   -4788,  -5094,  -5427,  -5791,
   -6187,  -6605,  -7030,  -7440,
   -7811,  -8116,  -8333,  -8447,
   -5340,  -5732,  -6033,  -6196,
   -6196,  -6033,  -5732,  -5340,
   -4911,  -4490,  -4108,  -3770,
   -3463,  -3158,  -2824,  -2438,
   -1995,  -1504,   -992,   -490,
     -26,    383,    732,   1030,
    1294,   1538,   1771,   1991,
    2185,   2336,   2428,   2453,
    2412,   2318,   2190,   2047,
    1904,   1763,   1621,   1467,
    1288,   1081,    849,    607,
     375,    174,     18,    -89,
    -156,   -199,   -239,   -286,
    -343,   -399,   -432,   -418,
    -341,   -199,     -6,    204,
     392,    520,    566,    529,
     431,    312,    220,    198,
     269,    431,    659,    906,
    1122,   1264,   1307,   1249,
    1113,    934,    750,    593,
     478,    404,    353,    303,
     234,    137,     15,   -116,
    -235,   -322,   -366,   -367,
    -334,   -285,   -238,   -202,
    -179,   -161,   -132,    -80,
       3,    116,    245,    374,
     484,    563,    609,    630,
     640,    657,    689,    738,
     790,    829,    835,    795,
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     -43,      3,     25,    -30,
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    -290,   -323,   -312,   -275,
    -228,   -176,   -106,      1,
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    1680,   1523,   1316,   1082,
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     -73,   -137,   -144,   -110,
     -75,    -58,    -52,    -26,
      36,    123,    201,    248,
     264,    274,    295,    322,
     333,    306,    246,    177,
     123,     89,     56,      5,
     -61,   -119,   -144,   -131,
     -99,    -74,    -65,    -52,
     -10,     66,    152,    213,
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     325,    332,    274,    177,
     100,     90,    133,    153,
      68,   -139,   -396,   -573,
    -573,   -396,   -139,     68,
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     280,    241,    231,    233,
     213,    152,     66,    -10,
     -52,    -65,    -74,    -99,
    -131,   -144,   -119,    -61,
       5,     56,     89,    123,
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     248,    201,    123,     36,
     -26,    -52,    -58,    -75,
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     531,    365,    121,    -74,
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    -161,   -108,    -63,    -48,
     -39,      7,    107,    239,
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     586,    636,    653,    617,
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    -134,    -40,    107,    303,
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     941,    806,    655,    467,
     254,     60,    -75,   -154,
    -205,   -236,   -228,   -159,
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     216,     98,      5,    -44,
     -71,   -101,   -128,   -116,
     -49,     43,    113,    152,
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     306,    139,   -149,   -393,
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     259,    287,    266,    199,
     131,     92,     66,     22,
     -43,    -93,   -102,    -78,
     -55,    -45,    -27,     21,
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     130,     84,     58,     30,
     -19,    -75,   -103,    -90,
     -60,    -45,    -42,    -16,
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     163,    198,    241,    233,
     157,     73,     60,    111,
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     164,    165,    125,     50,
     -16,    -42,    -45,    -60,
     -90,   -103,    -75,    -19,
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     181,    173,    148,     91,
      21,    -27,    -45,    -55,
     -78,   -102,    -93,    -43,
      22,     66,     92,    131,
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     226,    225,    233,    192,
      89,    -13,    -33,     22,
      46,    -63,   -277,   -437,
    -393,   -149,    139,    306,
     318,    276,    284,    351,
     398,    367,    279,    197,
     152,    113,     43,    -49,
    -116,   -128,   -101,    -71,
     -44,      5,     98,    216,
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     527,    524,    465,    370,
     273,    182,     79,    -43,
    -159,   -228,   -236,   -205,
    -154,    -75,     60,    254,
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    1062,   1130,   1092,    940,
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    -740,  -1252,  -1682,  -2015,
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     952,    880,    756,    618,
     448,    240,     45,    -87,
    -159,   -202,   -214,   -164,
     -55,     66,    167,    261,
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     362,    307,    222,    111,
      14,    -42,    -73,   -101,
    -109,    -67,     11,     81,
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     299,    260,    237,    215,
     149,     49,    -15,    -16,
     -19,    -70,   -101,    -23,
     116,    146,      1,   -159,
    -124,    102,    301,    306,
     179,     88,     83,     76,
       8,    -67,    -79,    -44,
     -24,    -25,      1,     68,
     129,    150,    154,    173,
     191,    170,    117,     72,
      48,     16,    -35,    -73,
     -72,    -51,    -38,    -27,
      11,     70,    113,    127,
     136,    157,    165,    134,
      84,     51,     33,     -1,
     -52,    -78,    -61,    -35,
     -31,    -23,     28,     97,
     127,    118,    128,    173,
     186,    120,     43,     52,
     108,     53,   -170,   -390,
    -390,   -170,     53,    108,
      52,     43,    120,    186,
     173,    128,    118,    127,
      97,     28,    -23,    -31,
     -35,    -61,    -78,    -52,
      -1,     33,     51,     84,
     134,    165,    157,    136,
     127,    113,     70,     11,
     -27,    -38,    -51,    -72,
     -73,    -35,     16,     48,
      72,    117,    170,    191,
     173,    154,    150,    129,
      68,      1,    -25,    -24,
     -44,    -79,    -67,      8,
      76,     83,     88,    179,
     306,    301,    102,   -124,
    -159,      1,    146,    116,
     -23,   -101,    -70,    -19,
     -16,    -15,     49,    149,
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     309,    261,    188,    131,
      81,     11,    -67,   -109,
    -101,    -73,    -42,     14,
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     411,    446,    431,    358,
     261,    167,     66,    -55,
    -164,   -214,   -202,   -159,
     -87,     45,    240,    448,
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     903,    728,    487,    207,
    -164,   -654,  -1166,  -1575,
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   -1585,  -1921,  -2358,  -2728,
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     692,    556,    387,    177,
     -10,   -119,   -175,   -201,
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     321,    263,    173,     63,
     -19,    -60,    -88,    -99,
     -59,     17,     82,    136,
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     -23,    -37,    -65,    -68,
      -8,     59,     83,    114,
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     192,    189,    -21,   -291,
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      78,     53,     32,    -21,
     -61,    -51,    -29,    -23,
      -1,     54,     99,    111,
     120,    139,    131,     88,
      50,     30,     -3,    -47,
     -61,    -43,    -30,    -21,
      16,     68,     95,    100,
     117,    129,    103,     58,
      35,     19,    -24,    -60,
     -50,    -25,    -24,    -12,
      46,     98,     95,     93,
     137,    149,     75,     21,
      72,     85,   -100,   -338,
    -338,   -100,     85,     72,
      21,     75,    149,    137,
      93,     95,     98,     46,
     -12,    -24,    -25,    -50,
     -60,    -24,     19,     35,
      58,    103,    129,    117,
     100,     95,     68,     16,
     -21,    -30,    -43,    -61,
     -47,     -3,     30,     50,
      88,    131,    139,    120,
     111,     99,     54,     -1,
     -23,    -29,    -51,    -61,
     -21,     32,     53,     78,
     138,    180,    158,    130,
     144,    129,     34,    -32,
      20,     45,   -118,   -325,
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     114,     83,     59,     -8,
     -68,    -65,    -37,    -23,
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     136,     82,     17,    -59,
     -99,    -88,    -60,    -19,
      63,    173,    263,    321,
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     162,     61,    -60,   -166,
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     806,    825,    689,    454,
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  -22142, -21889, -21625, -21348,
  -21061, -20762, -20452, -20133,
  -19804, -19466, -19119, -18763,
  -18399, -18027, -17647, -17259,
  -16865, -16463, -16055, -15640,
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    8319,   8806,   9290,   9771,
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   12121,  12579,  13032,  13480,
   13923,  14360,  14793,  15220,
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   17259,  17647,  18027,  18399,
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   23754,  23844,  23909,  23944,
   23944,  23909,  23844,  23754,
   23644,  23515,  23367,  23201,
   23018,  22820,  22608,  22382,
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   15220,  14793,  14360,  13923,
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   11659,  11193,  10723,  10249,
    9771,   9290,   8806,   8319,
    7829,   7336,   6841,   6344,
    5844,   5342,   4839,   4334,
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   -4334,  -4839,  -5342,  -5844,
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  -13923, -14360, -14793, -15220,
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  -17259, -17647, -18027, -18399,
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  -21348, -21625, -21889, -22142,
  -22382, -22608, -22820, -23018,
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  -23754, -23844, -23909, -23944,
  -13775, -13967, -14111, -14197,
  -14197, -14111, -13967, -13775,
  -13542, -13271, -12969, -12638,
  -12281, -11900, -11498, -11077,
  -10640, -10187,  -9721,  -9244,
   -8757,  -8262,  -7760,  -7253,
   -6743,  -6231,  -5719,  -5209,
   -4701,  -4199,  -3704,  -3218,
   -2744,  -2283,  -1841,  -1421,
   -1035,   -686,   -361,    -58,
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    1951,   1939,   1921,   1900,
    1874,   1847,   1819,   1790,
    1763,   1739,   1719,   1706,
    1706,   1720,   1741,   1769,
    1802,   1840,   1882,   1929,
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    2220,   2289,   2363,   2442,
    2525,   2615,   2710,   2813,
    2925,   3053,   3201,   3359,
    3522,   3688,   3854,   4017,
    4175,   4324,   4462,   4584,
    4678,   4743,   4791,   4825,
    4847,   4859,   4862,   4858,
    4846,   4829,   4806,   4778,
    4746,   4710,   4671,   4629,
    4585,   4539,   4492,   4444,
    4395,   4346,   4298,   4250,
    4204,   4159,   4118,   4080,
    4045,   4016,   3994,   3979,
    3979,   3994,   4016,   4045,
    4080,   4118,   4159,   4204,
    4250,   4298,   4346,   4395,
    4444,   4492,   4539,   4585,
    4629,   4671,   4710,   4746,
    4778,   4806,   4829,   4846,
    4858,   4862,   4859,   4847,
    4825,   4791,   4743,   4678,
    4584,   4462,   4324,   4175,
    4017,   3854,   3688,   3522,
    3359,   3201,   3053,   2925,
    2813,   2710,   2615,   2525,
    2442,   2363,   2289,   2220,
    2154,   2092,   2034,   1979,
    1929,   1882,   1840,   1802,
    1769,   1741,   1720,   1706,
    1706,   1719,   1739,   1763,
    1790,   1819,   1847,   1874,
    1900,   1921,   1939,   1951,
    1957,   1956,   1945,   1925,
    1894,   1849,   1790,   1713,
    1617,   1494,   1337,   1156,
     952,    729,    486,    224,
     -58,   -361,   -686,  -1035,
   -1421,  -1841,  -2283,  -2744,
   -3218,  -3704,  -4199,  -4701,
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   -7253,  -7760,  -8262,  -8757,
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    1229,   1160,   1111,   1070,
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     981,    992,   1006,   1021,
    1034,   1041,   1040,   1018,
     974,    930,    889,    844,
     789,    715,    623,    518,
     391,    247,    100,    -38,
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    -933,   -987,  -1018,  -1031,
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    -923,   -945,   -967,   -987,
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    -185,   -208,   -238,   -263,
    -278,   -276,   -247,   -161,
     -38,    100,    247,    391,
     518,    623,    715,    789,
     844,    889,    930,    974,
    1018,   1040,   1041,   1034,
    1021,   1006,    992,    981,
     981,    993,   1012,   1038,
    1070,   1111,   1160,   1229,
    1316,   1399,   1471,   1539,
    1605,   1676,   1745,   1804,
    1839,   1847,   1838,   1813,
    1775,   1716,   1635,   1543,
    1445,   1347,   1253,   1173,
    1115,   1073,   1043,   1026,
    1026,   1043,   1072,   1115,
    1180,   1252,   1313,   1352,
    1369,   1362,   1324,   1242,
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   -3683,  -4163,  -4615,  -5034,
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    1361,   1364,   1326,   1254,
    1163,   1070,    989,    927,
     894,    881,    890,    916,
     958,   1021,   1090,   1154,
    1201,   1224,   1227,   1201,
    1149,   1091,   1017,    918,
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     140,    149,    133,     96,
      43,     -8,    -67,   -147,
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    -563,   -472,   -398,   -336,
    -287,   -232,   -167,   -105,
     -58,    -31,    -13,    -10,
     -24,    -46,    -55,    -41,
     -19,     -9,     -2,     17,
      47,     85,    139,    199,
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     495,    486,    474,    459,
     444,    429,    415,    406,
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     459,    474,    486,    495,
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     404,    355,    299,    254,
     199,    139,     85,     47,
      17,     -2,     -9,    -19,
     -41,    -55,    -46,    -24,
     -10,    -13,    -31,    -58,
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    -336,   -398,   -472,   -563,
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    -421,   -436,   -470,   -504,
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    -607,   -593,   -569,   -532,
    -476,   -400,   -318,   -231,
    -147,    -67,     -8,     43,
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     123,    129,    153,    185,
     217,    254,    316,    392,
     480,    579,    692,    807,
     918,   1017,   1091,   1149,
    1201,   1227,   1224,   1201,
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     916,    890,    881,    894,
     927,    989,   1070,   1163,
    1254,   1326,   1364,   1361,
    1308,   1194,   1015,    763,
     436,     32,   -431,   -929,
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     790,    836,    860,    858,
     823,    770,    686,    581,
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      -5,    -62,    -99,   -127,
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    -272,   -248,   -212,   -168,
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     282,    277,    239,    175,
     115,     91,    134,    201,
     272,    321,    347,    363,
     382,    404,    413,    401,
     372,    326,    281,    241,
     193,    125,     74,     64,
      71,     71,     68,     69,
      67,     51,     51,     43,
      10,    -36,    -77,   -121,
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    -269,   -256,   -245,   -237,
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    -277,   -248,   -209,   -168,
    -121,    -77,    -36,     10,
      43,     51,     51,     67,
      69,     68,     71,     71,
      64,     74,    125,    193,
     241,    281,    326,    372,
     401,    413,    404,    382,
     363,    347,    321,    272,
     201,    134,     91,    115,
     175,    239,    277,    282,
     262,    230,    203,    161,
     101,     27,    -59,   -125,
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    -283,   -278,   -272,   -263,
    -264,   -273,   -289,   -310,
    -346,   -390,   -439,   -484,
    -513,   -528,   -529,   -530,
    -519,   -464,   -380,   -307,
    -251,   -205,   -162,   -139,
    -126,   -123,   -128,   -133,
    -127,    -99,    -62,     -5,
      92,    200,    323,    458,
     581,    686,    770,    823,
     858,    860,    836,    790,
     739,    705,    690,    698,
     734,    803,    896,   1009,
    1119,   1197,   1229,   1197,
    1091,    897,    610,    223,
    -241,   -744,  -1256,  -1761,
   -2231,  -2653,  -2988,  -3213,
   -1957,  -2399,  -2755,  -2997,
   -2997,  -2755,  -2399,  -1957,
   -1471,   -959,   -454,     18,
     405,    687,    865,    954,
     966,    921,    835,    743,
     671,    630,    621,    641,
     687,    750,    812,    853,
     867,    848,    796,    715,
     610,    500,    391,    299,
     226,    172,    139,    122,
     109,    117,    107,     78,
      37,    -22,    -91,   -167,
    -245,   -308,   -357,   -388,
    -398,   -398,   -399,   -376,
    -327,   -295,   -290,   -290,
    -304,   -328,   -355,   -382,
    -399,   -399,   -386,   -363,
    -322,   -268,   -209,   -154,
    -111,    -79,    -51,    -29,
     -31,    -34,    -20,     -4,
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     185,    237,    257,    236,
     197,    181,    211,    252,
     277,    268,    247,    240,
     247,    265,    281,    285,
     293,    299,    289,    269,
     232,    173,    121,    100,
      77,     41,     22,     15,
      11,     -2,      5,      7,
       2,    -16,    -43,    -76,
    -117,   -153,   -191,   -223,
    -249,   -258,   -257,   -251,
    -241,   -230,   -220,   -211,
    -211,   -220,   -230,   -241,
    -251,   -257,   -258,   -249,
    -223,   -191,   -153,   -117,
     -76,    -43,    -16,      2,
       7,      5,     -2,     11,
      15,     22,     41,     77,
     100,    121,    173,    232,
     269,    289,    299,    293,
     285,    281,    265,    247,
     240,    247,    268,    277,
     252,    211,    181,    197,
     236,    257,    237,    185,
     129,     85,     56,     27,
      -4,    -20,    -34,    -31,
     -29,    -51,    -79,   -111,
    -154,   -209,   -268,   -322,
    -363,   -386,   -399,   -399,
    -382,   -355,   -328,   -304,
    -290,   -290,   -295,   -327,
    -376,   -399,   -398,   -398,
    -388,   -357,   -308,   -245,
    -167,    -91,    -22,     37,
      78,    107,    117,    109,
     122,    139,    172,    226,
     299,    391,    500,    610,
     715,    796,    848,    867,
     853,    812,    750,    687,
     641,    621,    630,    671,
     743,    835,    921,    966,
     954,    865,    687,    405,
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   -1321,  -1795,  -2185,  -2456,
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     764,    884,    903,    850,
     747,    643,    567,    530,
     530,    560,    611,    657,
     675,    656,    597,    506,
     392,    267,    153,     63,
      -4,    -35,    -49,    -46,
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     184,    218,    235,    249,
     258,    249,    228,    197,
     165,    142,    129,    121,
     121,    127,    131,    125,
     102,     72,     24,    -37,
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    -367,   -323,   -262,   -203,
    -134,    -88,    -59,    -47,
     -46,    -49,    -35,     -4,
      63,    153,    267,    392,
     506,    597,    656,    675,
     657,    611,    560,    530,
     530,    567,    643,    747,
     850,    903,    884,    764,
     531,    166,   -302,   -814,
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  -12780, -12742, -12666, -12553,
  -12403, -12217, -11997, -11743,
  -11456, -11140, -10795, -10423,
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   -8237,  -7752,  -7256,  -6752,
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    -577,   -201,    154,    486,
     795,   1081,   1343,   1581,
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    2726,   2757,   2773,   2775,
    2766,   2746,   2716,   2679,
    2636,   2588,   2537,   2484,
    2430,   2378,   2326,   2278,
    2234,   2194,   2161,   2133,
    2112,   2098,   2092,   2093,
    2102,   2119,   2144,   2176,
    2215,   2261,   2312,   2370,
    2433,   2499,   2570,   2643,
    2718,   2795,   2872,   2948,
    3024,   3097,   3168,   3235,
    3298,   3357,   3411,   3459,
    3501,   3537,   3566,   3589,
    3604,   3614,   3616,   3612,
    3602,   3586,   3565,   3538,
    3507,   3472,   3434,   3392,
    3348,   3303,   3257,   3211,
    3166,   3121,   3078,   3038,
    3001,   2967,   2937,   2911,
    2890,   2874,   2863,   2858,
    2858,   2863,   2874,   2890,
    2911,   2937,   2967,   3001,
    3038,   3078,   3121,   3166,
    3211,   3257,   3303,   3348,
    3392,   3434,   3472,   3507,
    3538,   3565,   3586,   3602,
    3612,   3616,   3614,   3604,
    3589,   3566,   3537,   3501,
    3459,   3411,   3357,   3298,
    3235,   3168,   3097,   3024,
    2948,   2872,   2795,   2718,
    2643,   2570,   2499,   2433,
    2370,   2312,   2261,   2215,
    2176,   2144,   2119,   2102,
    2093,   2092,   2098,   2112,
    2133,   2161,   2194,   2234,
    2278,   2326,   2378,   2430,
    2484,   2537,   2588,   2636,
    2679,   2716,   2746,   2766,
    2775,   2773,   2757,   2726,
    2678,   2613,   2530,   2426,
    2302,   2156,   1987,   1796,
    1581,   1343,   1081,    795,
     486,    154,   -201,   -577,
    -973,  -1389,  -1823,  -2273,
   -2738,  -3216,  -3706,  -4204,
   -4709,  -5219,  -5731,  -6243,
   -6752,  -7256,  -7752,  -8237,
   -8710,  -9167,  -9607, -10026,
  -10423, -10795, -11140, -11456,
  -11743, -11997, -12217, -12403,
  -12553, -12666, -12742, -12780,
  -14967, -15112, -15210, -15259,
  -15259, -15210, -15112, -14967,
  -14776, -14540, -14263, -13946,
  -13593, -13208, -12794, -12354,
  -11893, -11414, -10922, -10419,
   -9910,  -9398,  -8886,  -8378,
   -7875,  -7380,  -6894,  -6421,
   -5959,  -5511,  -5076,  -4655,
   -4247,  -3853,  -3470,  -3099,
   -2737,  -2385,  -2040,  -1701,
   -1368,  -1039,   -714,   -391,
     -70,    249,    566,    881,
    1193,   1502,   1806,   2103,
    2394,   2674,   2944,   3200,
    3441,   3664,   3867,   4049,
    4208,   4342,   4449,   4529,
    4581,   4604,   4599,   4566,
    4505,   4418,   4307,   4173,
    4019,   3847,   3661,   3463,
    3258,   3048,   2838,   2631,
    2431,   2241,   2065,   1906,
    1767,   1650,   1557,   1491,
    1453,   1443,   1462,   1511,
    1588,   1693,   1824,   1979,
    2157,   2354,   2569,   2798,
    3038,   3286,   3538,   3792,
    4044,   4292,   4532,   4762,
    4979,   5183,   5370,   5541,
    5693,   5827,   5943,   6040,
    6120,   6182,   6229,   6262,
    6282,   6292,   6293,   6286,
    6275,   6260,   6244,   6228,
    6213,   6201,   6193,   6188,
    6188,   6193,   6201,   6213,
    6228,   6244,   6260,   6275,
    6286,   6293,   6292,   6282,
    6262,   6229,   6182,   6120,
    6040,   5943,   5827,   5693,
    5541,   5370,   5183,   4979,
    4762,   4532,   4292,   4044,
    3792,   3538,   3286,   3038,
    2798,   2569,   2354,   2157,
    1979,   1824,   1693,   1588,
    1511,   1462,   1443,   1453,
    1491,   1557,   1650,   1767,
    1906,   2065,   2241,   2431,
    2631,   2838,   3048,   3258,
    3463,   3661,   3847,   4019,
    4173,   4307,   4418,   4505,
    4566,   4599,   4604,   4581,
    4529,   4449,   4342,   4208,
    4049,   3867,   3664,   3441,
    3200,   2944,   2674,   2394,
    2103,   1806,   1502,   1193,
     881,    566,    249,    -70,
    -391,   -714,  -1039,  -1368,
   -1701,  -2040,  -2385,  -2737,
   -3099,  -3470,  -3853,  -4247,
   -4655,  -5076,  -5511,  -5959,
   -6421,  -6894,  -7380,  -7875,
   -8378,  -8886,  -9398,  -9910,
  -10419, -10922, -11414, -11893,
  -12354, -12794, -13208, -13593,
  -13946, -14263, -14540, -14776,
  -14967, -15112, -15210, -15259,
  -13027, -13226, -13361, -13429,
  -13429, -13361, -13226, -13027,
  -12768, -12454, -12090, -11683,
  -11240, -10769, -10277,  -9772,
   -9260,  -8748,  -8242,  -7746,
   -7264,  -6800,  -6354,  -5929,
   -5523,  -5135,  -4764,  -4407,
   -4061,  -3723,  -3391,  -3060,
   -2729,  -2396,  -2058,  -1716,
   -1368,  -1017,   -664,   -311,
      37,    378,    706,   1017,
    1305,   1568,   1798,   1994,
    2151,   2267,   2340,   2370,
    2358,   2305,   2215,   2090,
    1938,   1762,   1571,   1370,
    1167,    969,    784,    617,
     475,    364,    287,    248,
     248,    288,    368,    485,
     638,    821,   1031,   1262,
    1508,   1763,   2021,   2275,
    2520,   2752,   2966,   3157,
    3325,   3468,   3585,   3677,
    3746,   3793,   3824,   3840,
    3846,   3848,   3848,   3851,
    3860,   3880,   3911,   3956,
    4016,   4090,   4176,   4274,
    4379,   4489,   4599,   4704,
    4800,   4883,   4947,   4989,
    5005,   4992,   4949,   4874,
    4769,   4633,   4471,   4284,
    4078,   3858,   3629,   3399,
    3172,   2956,   2758,   2582,
    2435,   2320,   2242,   2202,
    2202,   2242,   2320,   2435,
    2582,   2758,   2956,   3172,
    3399,   3629,   3858,   4078,
    4284,   4471,   4633,   4769,
    4874,   4949,   4992,   5005,
    4989,   4947,   4883,   4800,
    4704,   4599,   4489,   4379,
    4274,   4176,   4090,   4016,
    3956,   3911,   3880,   3860,
    3851,   3848,   3848,   3846,
    3840,   3824,   3793,   3746,
    3677,   3585,   3468,   3325,
    3157,   2966,   2752,   2520,
    2275,   2021,   1763,   1508,
    1262,   1031,    821,    638,
     485,    368,    288,    248,
     248,    287,    364,    475,
     617,    784,    969,   1167,
    1370,   1571,   1762,   1938,
    2090,   2215,   2305,   2358,
    2370,   2340,   2267,   2151,
    1994,   1798,   1568,   1305,
    1017,    706,    378,     37,
    -311,   -664,  -1017,  -1368,
   -1716,  -2058,  -2396,  -2729,
   -3060,  -3391,  -3723,  -4061,
   -4407,  -4764,  -5135,  -5523,
   -5929,  -6354,  -6800,  -7264,
   -7746,  -8242,  -8748,  -9260,
   -9772, -10277, -10769, -11240,
  -11683, -12090, -12454, -12768,
  -13027, -13226, -13361, -13429,
  -12809, -13061, -13233, -13321,
  -13321, -13233, -13061, -12809,
  -12486, -12101, -11666, -11194,
  -10696, -10185,  -9673,  -9170,
   -8684,  -8222,  -7788,  -7383,
   -7008,  -6660,  -6334,  -6025,
   -5728,  -5436,  -5143,  -4843,
   -4533,  -4210,  -3872,  -3521,
   -3159,  -2791,  -2422,  -2058,
   -1708,  -1377,  -1073,   -802,
    -569,   -377,   -226,   -116,
     -43,     -4,      9,      4,
     -10,    -25,    -31,    -18,
      19,     87,    189,    327,
     500,    705,    937,   1188,
    1449,   1711,   1964,   2197,
    2401,   2568,   2691,   2766,
    2792,   2768,   2698,   2587,
    2444,   2276,   2096,   1913,
    1740,   1586,   1462,   1376,
    1334,   1339,   1394,   1496,
    1644,   1831,   2051,   2295,
    2554,   2819,   3080,   3330,
    3561,   3769,   3949,   4101,
    4224,   4320,   4394,   4451,
    4497,   4536,   4577,   4623,
    4680,   4749,   4834,   4931,
    5041,   5157,   5275,   5388,
    5488,   5568,   5620,   5637,
    5614,   5546,   5434,   5276,
    5075,   4838,   4571,   4284,
    3987,   3692,   3411,   3155,
    2936,   2762,   2642,   2581,
    2581,   2642,   2762,   2936,
    3155,   3411,   3692,   3987,
    4284,   4571,   4838,   5075,
    5276,   5434,   5546,   5614,
    5637,   5620,   5568,   5488,
    5388,   5275,   5157,   5041,
    4931,   4834,   4749,   4680,
    4623,   4577,   4536,   4497,
    4451,   4394,   4320,   4224,
    4101,   3949,   3769,   3561,
    3330,   3080,   2819,   2554,
    2295,   2051,   1831,   1644,
    1496,   1394,   1339,   1334,
    1376,   1462,   1586,   1740,
    1913,   2096,   2276,   2444,
    2587,   2698,   2768,   2792,
    2766,   2691,   2568,   2401,
    2197,   1964,   1711,   1449,
    1188,    937,    705,    500,
     327,    189,     87,     19,
     -18,    -31,    -25,    -10,
       4,      9,     -4,    -43,
    -116,   -226,   -377,   -569,
    -802,  -1073,  -1377,  -1708,
   -2058,  -2422,  -2791,  -3159,
   -3521,  -3872,  -4210,  -4533,
   -4843,  -5143,  -5436,  -5728,
   -6025,  -6334,  -6660,  -7008,
   -7383,  -7788,  -8222,  -8684,
   -9170,  -9673, -10185, -10696,
  -11194, -11666, -12101, -12486,
  -12809, -13061, -13233, -13321,
  -13403, -13692, -13892, -13995,
  -13995, -13892, -13692, -13403,
  -13037, -12610, -12138, -11638,
  -11126, -10616, -10120,  -9644,
   -9194,  -8769,  -8365,  -7978,
   -7599,  -7219,  -6830,  -6425,
   -5998,  -5548,  -5075,  -4584,
   -4083,  -3582,  -3093,  -2628,
   -2201,  -1822,  -1501,  -1242,
   -1048,   -916,   -840,   -809,
    -811,   -830,   -852,   -861,
    -843,   -786,   -684,   -533,
    -333,    -89,    189,    491,
     803,   1110,   1399,   1655,
    1870,   2036,   2149,   2211,
    2226,   2202,   2148,   2077,
    2002,   1933,   1880,   1852,
    1852,   1881,   1936,   2012,
    2100,   2189,   2269,   2329,
    2361,   2357,   2315,   2235,
    2120,   1980,   1825,   1668,
    1525,   1410,   1337,   1318,
    1362,   1474,   1654,   1899,
    2200,   2546,   2923,   3314,
    3703,   4075,   4415,   4711,
    4957,   5149,   5287,   5374,
    5419,   5430,   5420,   5398,
    5375,   5359,   5357,   5372,
    5402,   5443,   5489,   5531,
    5558,   5561,   5530,   5457,
    5337,   5170,   4958,   4708,
    4430,   4136,   3843,   3566,
    3321,   3123,   2984,   2912,
    2912,   2984,   3123,   3321,
    3566,   3843,   4136,   4430,
    4708,   4958,   5170,   5337,
    5457,   5530,   5561,   5558,
    5531,   5489,   5443,   5402,
    5372,   5357,   5359,   5375,
    5398,   5420,   5430,   5419,
    5374,   5287,   5149,   4957,
    4711,   4415,   4075,   3703,
    3314,   2923,   2546,   2200,
    1899,   1654,   1474,   1362,
    1318,   1337,   1410,   1525,
    1668,   1825,   1980,   2120,
    2235,   2315,   2357,   2361,
    2329,   2269,   2189,   2100,
    2012,   1936,   1881,   1852,
    1852,   1880,   1933,   2002,
    2077,   2148,   2202,   2226,
    2211,   2149,   2036,   1870,
    1655,   1399,   1110,    803,
     491,    189,    -89,   -333,
    -533,   -684,   -786,   -843,
    -861,   -852,   -830,   -811,
    -809,   -840,   -916,  -1048,
   -1242,  -1501,  -1822,  -2201,
   -2628,  -3093,  -3582,  -4083,
   -4584,  -5075,  -5548,  -5998,
   -6425,  -6830,  -7219,  -7599,
   -7978,  -8365,  -8769,  -9194,
   -9644, -10120, -10616, -11126,
  -11638, -12138, -12610, -13037,
  -13403, -13692, -13892, -13995,
   -9896, -10290, -10574, -10722,
  -10722, -10574, -10290,  -9896,
   -9424,  -8914,  -8402,  -7923,
   -7504,  -7161,  -6900,  -6715,
   -6591,  -6506,  -6436,  -6356,
   -6245,  -6087,  -5876,  -5608,
   -5291,  -4932,  -4546,  -4142,
   -3732,  -3323,  -2916,  -2512,
   -2106,  -1695,  -1277,   -850,
    -421,      3,    409,    781,
    1103,   1360,   1542,   1646,
    1674,   1637,   1555,   1449,
    1346,   1268,   1237,   1264,
    1355,   1505,   1699,   1917,
    2134,   2326,   2470,   2550,
    2558,   2496,   2375,   2214,
    2035,   1864,   1724,   1632,
    1599,   1625,   1701,   1812,
    1935,   2046,   2124,   2151,
    2118,   2023,   1875,   1692,
    1497,   1315,   1172,   1089,
    1080,   1152,   1299,   1509,
    1762,   2034,   2300,   2537,
    2726,   2856,   2923,   2931,
    2888,   2809,   2709,   2602,
    2501,   2413,   2341,   2284,
    2239,   2200,   2161,   2122,
    2083,   2050,   2031,   2036,
    2076,   2160,   2291,   2466,
    2676,   2905,   3130,   3324,
    3463,   3523,   3489,   3353,
    3120,   2806,   2437,   2046,
    1671,   1349,   1115,    991,
     991,   1115,   1349,   1671,
    2046,   2437,   2806,   3120,
    3353,   3489,   3523,   3463,
    3324,   3130,   2905,   2676,
    2466,   2291,   2160,   2076,
    2036,   2031,   2050,   2083,
    2122,   2161,   2200,   2239,
    2284,   2341,   2413,   2501,
    2602,   2709,   2809,   2888,
    2931,   2923,   2856,   2726,
    2537,   2300,   2034,   1762,
    1509,   1299,   1152,   1080,
    1089,   1172,   1315,   1497,
    1692,   1875,   2023,   2118,
    2151,   2124,   2046,   1935,
    1812,   1701,   1625,   1599,
    1632,   1724,   1864,   2035,
    2214,   2375,   2496,   2558,
    2550,   2470,   2326,   2134,
    1917,   1699,   1505,   1355,
    1264,   1237,   1268,   1346,
    1449,   1555,   1637,   1674,
    1646,   1542,   1360,   1103,
     781,    409,      3,   -421,
    -850,  -1277,  -1695,  -2106,
   -2512,  -2916,  -3323,  -3732,
   -4142,  -4546,  -4932,  -5291,
   -5608,  -5876,  -6087,  -6245,
   -6356,  -6436,  -6506,  -6591,
   -6715,  -6900,  -7161,  -7504,
   -7923,  -8402,  -8914,  -9424,
   -9896, -10290, -10574, -10722,
   -7185,  -7596,  -7895,  -8052,
   -8052,  -7895,  -7596,  -7185,
   -6701,  -6189,  -5694,  -5257,
   -4908,  -4667,  -4538,  -4515,
   -4577,  -4697,  -4846,  -4991,
   -5106,  -5172,  -5178,  -5119,
   -5002,  -4837,  -4636,  -4413,
   -4178,  -3939,  -3697,  -3450,
   -3193,  -2920,  -2629,  -2317,
   -1989,  -1656,  -1333,  -1037,
    -788,   -604,   -496,   -470,
    -520,   -635,   -794,   -968,
   -1128,  -1247,  -1300,  -1274,
   -1163,   -974,   -725,   -440,
    -151,    112,    321,    457,
     509,    479,    379,    231,
      62,    -98,   -223,   -291,
    -291,   -222,    -95,     70,
     248,    411,    531,    588,
     572,    481,    326,    128,
     -84,   -279,   -427,   -500,
    -482,   -366,   -155,    136,
     483,    859,   1233,   1579,
    1874,   2106,   2270,   2370,
    2418,   2430,   2425,   2421,
    2430,   2463,   2523,   2608,
    2712,   2830,   2954,   3081,
    3213,   3354,   3513,   3704,
    3936,   4220,   4558,   4947,
    5374,   5818,   6251,   6641,
    6957,   7169,   7259,   7216,
    7047,   6768,   6410,   6013,
    5621,   5280,   5028,   4894,
    4894,   5028,   5280,   5621,
    6013,   6410,   6768,   7047,
    7216,   7259,   7169,   6957,
    6641,   6251,   5818,   5374,
    4947,   4558,   4220,   3936,
    3704,   3513,   3354,   3213,
    3081,   2954,   2830,   2712,
    2608,   2523,   2463,   2430,
    2421,   2425,   2430,   2418,
    2370,   2270,   2106,   1874,
    1579,   1233,    859,    483,
     136,   -155,   -366,   -482,
    -500,   -427,   -279,    -84,
     128,    326,    481,    572,
     588,    531,    411,    248,
      70,    -95,   -222,   -291,
    -291,   -223,    -98,     62,
     231,    379,    479,    509,
     457,    321,    112,   -151,
    -440,   -725,   -974,  -1163,
   -1274,  -1300,  -1247,  -1128,
    -968,   -794,   -635,   -520,
    -470,   -496,   -604,   -788,
   -1037,  -1333,  -1656,  -1989,
   -2317,  -2629,  -2920,  -3193,
   -3450,  -3697,  -3939,  -4178,
   -4413,  -4636,  -4837,  -5002,
   -5119,  -5178,  -5172,  -5106,
   -4991,  -4846,  -4697,  -4577,
   -4515,  -4538,  -4667,  -4908,
   -5257,  -5694,  -6189,  -6701,
   -7185,  -7596,  -7895,  -8052,
   -2946,  -3276,  -3520,  -3649,
   -3649,  -3520,  -3276,  -2946,
   -2567,  -2179,  -1823,  -1532,
   -1328,  -1219,  -1200,  -1253,
   -1349,  -1454,  -1534,  -1560,
   -1508,  -1370,  -1147,   -851,
    -505,   -135,    230,    567,
     856,   1088,   1265,   1395,
    1494,   1581,   1674,   1787,
    1928,   2095,   2281,   2468,
    2639,   2771,   2849,   2861,
    2806,   2692,   2535,   2359,
    2191,   2058,   1979,   1967,
    2024,   2137,   2286,   2440,
    2563,   2623,   2590,   2447,
    2188,   1821,   1371,    869,
     357,   -124,   -535,   -848,
   -1047,  -1131,  -1113,  -1021,
    -890,   -760,   -669,   -649,
    -720,   -891,  -1153,  -1487,
   -1863,  -2246,  -2599,  -2892,
   -3100,  -3214,  -3232,  -3166,
   -3037,  -2871,  -2695,  -2532,
   -2399,  -2305,  -2249,  -2220,
   -2203,  -2177,  -2126,  -2034,
   -1893,  -1705,  -1478,  -1228,
    -976,   -743,   -545,   -394,
    -292,   -234,   -201,   -173,
    -123,    -27,    136,    375,
     692,   1073,   1494,   1925,
    2329,   2670,   2918,   3054,
    3071,   2976,   2790,   2546,
    2282,   2039,   1854,   1754,
    1754,   1854,   2039,   2282,
    2546,   2790,   2976,   3071,
    3054,   2918,   2670,   2329,
    1925,   1494,   1073,    692,
     375,    136,    -27,   -123,
    -173,   -201,   -234,   -292,
    -394,   -545,   -743,   -976,
   -1228,  -1478,  -1705,  -1893,
   -2034,  -2126,  -2177,  -2203,
   -2220,  -2249,  -2305,  -2399,
   -2532,  -2695,  -2871,  -3037,
   -3166,  -3232,  -3214,  -3100,
   -2892,  -2599,  -2246,  -1863,
   -1487,  -1153,   -891,   -720,
    -649,   -669,   -760,   -890,
   -1021,  -1113,  -1131,  -1047,
    -848,   -535,   -124,    357,
     869,   1371,   1821,   2188,
    2447,   2590,   2623,   2563,
    2440,   2286,   2137,   2024,
    1967,   1979,   2058,   2191,
    2359,   2535,   2692,   2806,
    2861,   2849,   2771,   2639,
    2468,   2281,   2095,   1928,
    1787,   1674,   1581,   1494,
    1395,   1265,   1088,    856,
     567,    230,   -135,   -505,
    -851,  -1147,  -1370,  -1508,
   -1560,  -1534,  -1454,  -1349,
   -1253,  -1200,  -1219,  -1328,
   -1532,  -1823,  -2179,  -2567,
   -2946,  -3276,  -3520,  -3649,
  -12803, -13002, -13147, -13223,
  -13223, -13147, -13002, -12803,
  -12572, -12329, -12094, -11884,
  -11707, -11563, -11446, -11339,
  -11226, -11085, -10896, -10647,
  -10330,  -9946,  -9504,  -9020,
   -8515,  -8012,  -7532,  -7091,
   -6698,  -6354,  -6053,  -5780,
   -5517,  -5244,  -4942,  -4596,
   -4201,  -3756,  -3272,  -2763,
   -2251,  -1758,  -1304,   -906,
    -571,   -301,    -89,     81,
     229,    374,    536,    731,
     966,   1241,   1549,   1873,
    2194,   2492,   2746,   2942,
    3071,   3135,   3142,   3106,
    3050,   2994,   2959,   2960,
    3007,   3100,   3231,   3387,
    3547,   3692,   3802,   3863,
    3867,   3815,   3716,   3586,
    3444,   3314,   3215,   3163,
    3166,   3225,   3333,   3475,
    3630,   3779,   3901,   3982,
    4014,   3996,   3938,   3854,
    3764,   3689,   3649,   3659,
    3727,   3852,   4027,   4236,
    4458,   4672,   4859,   5001,
    5092,   5129,   5122,   5084,
    5036,   4997,   4987,   5021,
    5107,   5243,   5422,   5628,
    5840,   6037,   6199,   6310,
    6362,   6355,   6295,   6199,
    6086,   5977,   5891,   5844,
    5844,   5891,   5977,   6086,
    6199,   6295,   6355,   6362,
    6310,   6199,   6037,   5840,
    5628,   5422,   5243,   5107,
    5021,   4987,   4997,   5036,
    5084,   5122,   5129,   5092,
    5001,   4859,   4672,   4458,
    4236,   4027,   3852,   3727,
    3659,   3649,   3689,   3764,
    3854,   3938,   3996,   4014,
    3982,   3901,   3779,   3630,
    3475,   3333,   3225,   3166,
    3163,   3215,   3314,   3444,
    3586,   3716,   3815,   3867,
    3863,   3802,   3692,   3547,
    3387,   3231,   3100,   3007,
    2960,   2959,   2994,   3050,
    3106,   3142,   3135,   3071,
    2942,   2746,   2492,   2194,
    1873,   1549,   1241,    966,
     731,    536,    374,    229,
      81,    -89,   -301,   -571,
    -906,  -1304,  -1758,  -2251,
   -2763,  -3272,  -3756,  -4201,
   -4596,  -4942,  -5244,  -5517,
   -5780,  -6053,  -6354,  -6698,
   -7091,  -7532,  -8012,  -8515,
   -9020,  -9504,  -9946, -10330,
  -10647, -10896, -11085, -11226,
  -11339, -11446, -11563, -11707,
  -11884, -12094, -12329, -12572,
  -12803, -13002, -13147, -13223,
   -9202,  -9566,  -9825,  -9959,
   -9959,  -9825,  -9566,  -9202,
   -8758,  -8265,  -7753,  -7250,
   -6780,  -6357,  -5991,  -5682,
   -5421,  -5199,  -5000,  -4811,
   -4618,  -4413,  -4191,  -3953,
   -3702,  -3445,  -3189,  -2941,
   -2706,  -2486,  -2279,  -2081,
   -1887,  -1689,  -1482,  -1263,
   -1032,   -792,   -552,   -321,
    -109,     72,    214,    315,
     374,    398,    396,    384,
     376,    387,    429,    509,
     629,    783,    960,   1145,
    1321,   1469,   1576,   1630,
    1629,   1575,   1478,   1353,
    1220,   1098,   1005,    955,
     955,   1006,   1101,   1227,
    1367,   1503,   1616,   1693,
    1723,   1704,   1641,   1545,
    1431,   1317,   1222,   1161,
    1145,   1180,   1264,   1391,
    1549,   1724,   1899,   2060,
    2198,   2305,   2381,   2428,
    2455,   2471,   2487,   2511,
    2551,   2609,   2684,   2773,
    2869,   2964,   3052,   3126,
    3185,   3230,   3264,   3292,
    3322,   3358,   3404,   3459,
    3516,   3567,   3597,   3591,
    3534,   3414,   3223,   2960,
    2634,   2258,   1856,   1455,
    1086,    778,    556,    440,
     440,    556,    778,   1086,
    1455,   1856,   2258,   2634,
    2960,   3223,   3414,   3534,
    3591,   3597,   3567,   3516,
    3459,   3404,   3358,   3322,
    3292,   3264,   3230,   3185,
    3126,   3052,   2964,   2869,
    2773,   2684,   2609,   2551,
    2511,   2487,   2471,   2455,
    2428,   2381,   2305,   2198,
    2060,   1899,   1724,   1549,
    1391,   1264,   1180,   1145,
    1161,   1222,   1317,   1431,
    1545,   1641,   1704,   1723,
    1693,   1616,   1503,   1367,
    1227,   1101,   1006,    955,
     955,   1005,   1098,   1220,
    1353,   1478,   1575,   1629,
    1630,   1576,   1469,   1321,
    1145,    960,    783,    629,
     509,    429,    387,    376,
     384,    396,    398,    374,
     315,    214,     72,   -109,
    -321,   -552,   -792,  -1032,
   -1263,  -1482,  -1689,  -1887,
   -2081,  -2279,  -2486,  -2706,
   -2941,  -3189,  -3445,  -3702,
   -3953,  -4191,  -4413,  -4618,
   -4811,  -5000,  -5199,  -5421,
   -5682,  -5991,  -6357,  -6780,
   -7250,  -7753,  -8265,  -8758,
   -9202,  -9566,  -9825,  -9959,
  -11375, -11720, -11964, -12090,
  -12090, -11964, -11720, -11375,
  -10950, -10470,  -9963,  -9451,
   -8955,  -8490,  -8063,  -7677,
   -7327,  -7005,  -6700,  -6401,
   -6098,  -5784,  -5455,  -5111,
   -4755,  -4394,  -4032,  -3676,
   -3332,  -3001,  -2685,  -2382,
   -2087,  -1797,  -1509,  -1220,
    -931,   -643,   -362,    -95,
     151,    370,    557,    709,
     829,    920,    993,   1056,
    1120,   1197,   1294,   1414,
    1556,   1715,   1881,   2042,
    2182,   2289,   2352,   2364,
    2326,   2241,   2122,   1982,
    1839,   1712,   1617,   1566,
    1566,   1618,   1715,   1847,
    1998,   2151,   2290,   2400,
    2472,   2502,   2490,   2445,
    2377,   2300,   2230,   2179,
    2159,   2173,   2225,   2311,
    2422,   2548,   2680,   2805,
    2916,   3007,   3076,   3125,
    3158,   3180,   3200,   3221,
    3249,   3284,   3327,   3374,
    3419,   3459,   3488,   3503,
    3503,   3490,   3468,   3441,
    3415,   3393,   3377,   3367,
    3358,   3340,   3303,   3234,
    3123,   2959,   2738,   2460,
    2133,   1770,   1391,   1019,
     681,    402,    202,     98,
      98,    202,    402,    681,
    1019,   1391,   1770,   2133,
    2460,   2738,   2959,   3123,
    3234,   3303,   3340,   3358,
    3367,   3377,   3393,   3415,
    3441,   3468,   3490,   3503,
    3503,   3488,   3459,   3419,
    3374,   3327,   3284,   3249,
    3221,   3200,   3180,   3158,
    3125,   3076,   3007,   2916,
    2805,   2680,   2548,   2422,
    2311,   2225,   2173,   2159,
    2179,   2230,   2300,   2377,
    2445,   2490,   2502,   2472,
    2400,   2290,   2151,   1998,
    1847,   1715,   1618,   1566,
    1566,   1617,   1712,   1839,
    1982,   2122,   2241,   2326,
    2364,   2352,   2289,   2182,
    2042,   1881,   1715,   1556,
    1414,   1294,   1197,   1120,
    1056,    993,    920,    829,
     709,    557,    370,    151,
     -95,   -362,   -643,   -931,
   -1220,  -1509,  -1797,  -2087,
   -2382,  -2685,  -3001,  -3332,
   -3676,  -4032,  -4394,  -4755,
   -5111,  -5455,  -5784,  -6098,
   -6401,  -6700,  -7005,  -7327,
   -7677,  -8063,  -8490,  -8955,
   -9451,  -9963, -10470, -10950,
  -11375, -11720, -11964, -12090,
  -11010, -11365, -11617, -11747,
  -11747, -11617, -11365, -11010,
  -10576, -10088,  -9576,  -9065,
   -8574,  -8118,  -7702,  -7326,
   -6983,  -6660,  -6346,  -6026,
   -5691,  -5334,  -4954,  -4554,
   -4141,  -3727,  -3321,  -2934,
   -2575,  -2247,  -1951,  -1684,
   -1441,  -1214,   -995,   -777,
    -557,   -333,   -108,    115,
     329,    529,    711,    871,
    1012,   1138,   1257,   1377,
    1508,   1659,   1834,   2034,
    2254,   2484,   2709,   2912,
    3076,   3185,   3227,   3196,
    3096,   2934,   2729,   2502,
    2279,   2084,   1940,   1863,
    1863,   1940,   2086,   2285,
    2515,   2753,   2974,   3156,
    3284,   3349,   3349,   3290,
    3185,   3049,   2902,   2760,
    2639,   2549,   2494,   2475,
    2486,   2520,   2567,   2618,
    2664,   2701,   2727,   2744,
    2757,   2770,   2788,   2815,
    2853,   2899,   2949,   2994,
    3028,   3040,   3024,   2977,
    2897,   2789,   2659,   2516,
    2371,   2233,   2108,   1998,
    1901,   1809,   1712,   1596,
    1446,   1251,   1002,    698,
     344,    -47,   -454,   -853,
   -1217,  -1519,  -1735,  -1847,
   -1847,  -1735,  -1519,  -1217,
    -853,   -454,    -47,    344,
     698,   1002,   1251,   1446,
    1596,   1712,   1809,   1901,
    1998,   2108,   2233,   2371,
    2516,   2659,   2789,   2897,
    2977,   3024,   3040,   3028,
    2994,   2949,   2899,   2853,
    2815,   2788,   2770,   2757,
    2744,   2727,   2701,   2664,
    2618,   2567,   2520,   2486,
    2475,   2494,   2549,   2639,
    2760,   2902,   3049,   3185,
    3290,   3349,   3349,   3284,
    3156,   2974,   2753,   2515,
    2285,   2086,   1940,   1863,
    1863,   1940,   2084,   2279,
    2502,   2729,   2934,   3096,
    3196,   3227,   3185,   3076,
    2912,   2709,   2484,   2254,
    2034,   1834,   1659,   1508,
    1377,   1257,   1138,   1012,
     871,    711,    529,    329,
     115,   -108,   -333,   -557,
    -777,   -995,  -1214,  -1441,
   -1684,  -1951,  -2247,  -2575,
   -2934,  -3321,  -3727,  -4141,
   -4554,  -4954,  -5334,  -5691,
   -6026,  -6346,  -6660,  -6983,
   -7326,  -7702,  -8118,  -8574,
   -9065,  -9576, -10088, -10576,
  -11010, -11365, -11617, -11747,
   -9937, -10252, -10472, -10585,
  -10585, -10472, -10252,  -9937,
   -9544,  -9092,  -8601,  -8090,
   -7578,  -7078,  -6601,  -6150,
   -5729,  -5335,  -4966,  -4617,
   -4285,  -3966,  -3659,  -3365,
   -3084,  -2818,  -2571,  -2342,
   -2132,  -1938,  -1756,  -1582,
   -1410,  -1233,  -1047,   -849,
    -636,   -411,   -179,     57,
     289,    509,    713,    895,
    1054,   1191,   1309,   1413,
    1508,   1602,   1699,   1801,
    1910,   2023,   2134,   2236,
    2323,   2387,   2422,   2424,
    2396,   2339,   2263,   2178,
    2094,   2025,   1980,   1968,
    1993,   2055,   2150,   2272,
    2408,   2549,   2683,   2800,
    2892,   2957,   2993,   3005,
    2998,   2979,   2958,   2940,
    2931,   2933,   2948,   2970,
    2996,   3020,   3035,   3037,
    3021,   2987,   2937,   2875,
    2806,   2736,   2673,   2622,
    2585,   2565,   2559,   2564,
    2574,   2583,   2584,   2572,
    2542,   2492,   2421,   2329,
    2217,   2088,   1942,   1778,
    1594,   1388,   1155,    889,
     588,    250,   -125,   -531,
    -959,  -1394,  -1821,  -2219,
   -2569,  -2851,  -3049,  -3151,
   -3151,  -3049,  -2851,  -2569,
   -2219,  -1821,  -1394,   -959,
    -531,   -125,    250,    588,
     889,   1155,   1388,   1594,
    1778,   1942,   2088,   2217,
    2329,   2421,   2492,   2542,
    2572,   2584,   2583,   2574,
    2564,   2559,   2565,   2585,
    2622,   2673,   2736,   2806,
    2875,   2937,   2987,   3021,
    3037,   3035,   3020,   2996,
    2970,   2948,   2933,   2931,
    2940,   2958,   2979,   2998,
    3005,   2993,   2957,   2892,
    2800,   2683,   2549,   2408,
    2272,   2150,   2055,   1993,
    1968,   1980,   2025,   2094,
    2178,   2263,   2339,   2396,
    2424,   2422,   2387,   2323,
    2236,   2134,   2023,   1910,
    1801,   1699,   1602,   1508,
    1413,   1309,   1191,   1054,
     895,    713,    509,    289,
      57,   -179,   -411,   -636,
    -849,  -1047,  -1233,  -1410,
   -1582,  -1756,  -1938,  -2132,
   -2342,  -2571,  -2818,  -3084,
   -3365,  -3659,  -3966,  -4285,
   -4617,  -4966,  -5335,  -5729,
   -6150,  -6601,  -7078,  -7578,
   -8090,  -8601,  -9092,  -9544,
   -9937, -10252, -10472, -10585,
   -7063,  -7314,  -7486,  -7574,
   -7574,  -7486,  -7314,  -7063,
   -6739,  -6354,  -5918,  -5443,
   -4943,  -4431,  -3920,  -3422,
   -2948,  -2508,  -2108,  -1754,
   -1450,  -1196,   -991,   -833,
    -718,   -640,   -593,   -570,
    -565,   -570,   -580,   -590,
    -595,   -592,   -579,   -555,
    -520,   -476,   -423,   -364,
    -301,   -237,   -174,   -114,
     -58,     -7,     39,     80,
     117,    151,    184,    218,
     255,    296,    344,    398,
     459,    528,    604,    685,
     771,    858,    946,   1032,
    1113,   1188,   1256,   1314,
    1363,   1403,   1433,   1456,
    1472,   1484,   1493,   1502,
    1512,   1527,   1546,   1572,
    1604,   1643,   1688,   1738,
    1792,   1848,   1903,   1956,
    2006,   2050,   2088,   2120,
    2146,   2166,   2181,   2195,
    2208,   2223,   2243,   2269,
    2304,   2348,   2401,   2462,
    2529,   2599,   2667,   2729,
    2778,   2808,   2811,   2781,
    2712,   2599,   2436,   2222,
    1955,   1636,   1270,    860,
     415,    -57,   -544,  -1035,
   -1516,  -1974,  -2396,  -2769,
   -3083,  -3327,  -3495,  -3579,
   -3579,  -3495,  -3327,  -3083,
   -2769,  -2396,  -1974,  -1516,
   -1035,   -544,    -57,    415,
     860,   1270,   1636,   1955,
    2222,   2436,   2599,   2712,
    2781,   2811,   2808,   2778,
    2729,   2667,   2599,   2529,
    2462,   2401,   2348,   2304,
    2269,   2243,   2223,   2208,
    2195,   2181,   2166,   2146,
    2120,   2088,   2050,   2006,
    1956,   1903,   1848,   1792,
    1738,   1688,   1643,   1604,
    1572,   1546,   1527,   1512,
    1502,   1493,   1484,   1472,
    1456,   1433,   1403,   1363,
    1314,   1256,   1188,   1113,
    1032,    946,    858,    771,
     685,    604,    528,    459,
     398,    344,    296,    255,
     218,    184,    151,    117,
      80,     39,     -7,    -58,
    -114,   -174,   -237,   -301,
    -364,   -423,   -476,   -520,
    -555,   -579,   -592,   -595,
    -590,   -580,   -570,   -565,
    -570,   -593,   -640,   -718,
    -833,   -991,  -1196,  -1450,
   -1754,  -2108,  -2508,  -2948,
   -3422,  -3920,  -4431,  -4943,
   -5443,  -5918,  -6354,  -6739,
   -7063,  -7314,  -7486,  -7574,
   -3720,  -3997,  -4187,  -4284,
   -4284,  -4187,  -3997,  -3720,
   -3368,  -2952,  -2487,  -1990,
   -1478,   -968,   -476,    -17,
     396,    753,   1046,   1270,
    1425,   1510,   1531,   1494,
    1407,   1281,   1126,    954,
     775,    600,    438,    295,
     177,     89,     30,      2,
       2,     27,     72,    131,
     200,    272,    343,    408,
     462,    505,    534,    549,
     551,    541,    523,    499,
     473,    447,    425,    408,
     399,    398,    407,    423,
     446,    474,    505,    535,
     563,    587,    604,    612,
     612,    604,    587,    563,
     535,    505,    474,    446,
     423,    407,    398,    399,
     408,    425,    447,    473,
     499,    523,    541,    551,
     549,    534,    505,    462,
     408,    343,    272,    200,
     131,     72,     27,      2,
       2,     30,     89,    177,
     295,    438,    600,    775,
     954,   1126,   1281,   1407,
    1494,   1531,   1510,   1425,
    1270,   1046,    753,    396,
     -17,   -476,   -968,  -1478,
   -1990,  -2487,  -2952,  -3368,
   -3720,  -3997,  -4187,  -4284,
   -4284,  -4187,  -3997,  -3720,
   -3368,  -2952,  -2487,  -1990,
   -1478,   -968,   -476,    -17,
     396,    753,   1046,   1270,
    1425,   1510,   1531,   1494,
    1407,   1281,   1126,    954,
     775,    600,    438,    295,
     177,     89,     30,      2,
       2,     27,     72,    131,
     200,    272,    343,    408,
     462,    505,    534,    549,
     551,    541,    523,    499,
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    -420,   -424,   -429,   -434,
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    -478,   -483,   -488,   -493,
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    -537,   -542,   -547,   -552,
    -557,   -562,   -567,   -572,
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    -694,   -699,   -704,   -709,
    -714,   -719,   -724,   -729,
    -734,   -738,   -743,   -748,
    -753,   -758,   -763,   -768,
    -773,   -778,   -783,   -787,
    -792,   -797,   -802,   -807,
    -812,   -817,   -822,   -827,
    -832,   -837,   -841,   -846,
    -851,   -856,   -861,   -866,
    -871,   -876,   -881,   -886,
    -890,   -895,   -900,   -905,
    -910,   -915,   -920,   -925,
    -930,   -935,   -940,   -944,
    -949,   -954,   -959,   -964,
    -969,   -974,   -979,   -984,
    -989,   -994,   -998,  -1003,
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     621,    149,   -212,   -406,
    -406,   -209,    153,    626,
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     633,    161,   -199,   -394,
    -393,   -197,    165,    638,
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    2183,   1988,   1627,   1156,
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    -381,   -185,    177,    650,
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      83,     81,     79,     77,
      75,     73,     71,     69,
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      59,     57,     55,     53,
      51,     49,     47,     45,
      43,     41,     39,     37,
      35,     33,     31,     29,
      27,     25,     23,     21,
      19,     17,     15,     13,
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    -439,   -124,    191,    504,
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    3997,   4032,   4044,   4035,
    4003,   3950,   3876,   3782,
    3667,   3533,   3381,   3212,
    3026,   2825,   2611,   2383,
    2144,   1896,   1638,   1373,
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     -11,   -290,   -566,   -838,
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    6536,   6486,   6381,   6223,
    6015,   5758,   5457,   5116,
    4737,   4327,   3890,   3432,
    2958,   2473,   1984,   1496,
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    -732,  -1100,  -1432,  -1725,
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   -1390,  -1082,   -749,   -395,
     -26,    354,    740,   1127,
    1510,   1883,   2243,   2585,
    2905,   3198,   3462,   3692,
    3887,   4045,   4162,   4240,
    4275,   4269,   4222,   4134,
    4007,   3842,   3642,   3410,
    3148,   2860,   2549,   2219,
    1874,   1518,   1156,    791,
     429,     73,   -273,   -606,
    -920,  -1214,  -1484,  -1726,
   -1940,  -2123,  -2273,  -2389,
   -2470,  -2517,  -2530,  -2508,
   -2453,  -2366,  -2250,  -2105,
   -1936,  -1743,  -1531,  -1302,
   -1059,   -807,   -548,   -286,
     -24,    233,    484,    724,
     950,   1161,   1352,   1523,
    1670,   1793,   1890,   1960,
    2002,   2016,   2002,   1961,
    1893,   1799,   1681,   1541,
    1380,   1200,   1003,    793,
     571,    341,    105,   -134,
    -373,   -610,   -843,  -1067,
   -1282,  -1485,  -1674,  -1847,
   -2003,  -2140,  -2257,  -2354,
   -2430,  -2485,  -2519,  -2532,
   -2525,  -2498,  -2453,  -2391,
   -2313,  -2221,  -2117,  -2002,
   -1879,  -1749,  -1614,  -1477,
   -1339,  -1203,  -1070,   -942,
    -822,   -709,   -606,   -515,
    -435,   -368,   -315,   -276,
    -252,   -242,   -246,   -264,
    -296,   -341,   -398,   -467,
    -545,   -633,   -729,   -831,
    -939,  -1050,  -1165,  -1280,
   -1396,  -1510,  -1622,  -1731,
   -1835,  -1933,  -2026,  -2112,
   -2190,  -2261,  -2324,  -2379,
   -2426,  -2465,  -2496,  -2520,
   -2536,  -2547,  -2552,  -2551,
   -2546,  -2537,  -2526,  -2512,
   -2496,  -2480,  -2464,  -2448,
   -2433,  -2420,  -2410,  -2401,
   -2395,  -2393,  -2393,  -2396,
   -2402,  -2412,  -2423,  -2437,
   -2454,  -2471,  -2490,  -2510,
   -1811,  -1828,  -1844,  -1859,
   -1873,  -1808,  -1664,  -1445,
   -1159,   -811,   -410,     35,
     513,   1014,   1526,   2038,
    2538,   3015,   3460,   3862,
    4212,   4504,   4731,   4888,
    4972,   4982,   4918,   4782,
    4577,   4307,   3978,   3599,
    3176,   2720,   2241,   1747,
    1251,    762,    290,   -154,
    -562,   -926,  -1238,  -1492,
   -1685,  -1812,  -1871,  -1863,
   -1789,  -1651,  -1452,  -1199,
    -897,   -554,   -178,    222,
     638,   1060,   1478,   1882,
    2265,   2618,   2932,   3202,
    3422,   3587,   3693,   3740,
    3725,   3650,   3517,   3329,
    3089,   2805,   2481,   2125,
    1745,   1348,    944,    541,
     146,   -231,   -583,   -903,
   -1186,  -1424,  -1615,  -1755,
   -1842,  -1875,  -1853,  -1780,
   -1656,  -1486,  -1274,  -1026,
    -747,   -444,   -126,    202,
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    1721,   1954,   2149,   2304,
    2415,   2479,   2496,   2466,
    2389,   2268,   2105,   1905,
    1671,   1410,   1126,    826,
     516,    202,   -108,   -408,
    -693,   -956,  -1194,  -1400,
   -1573,  -1708,  -1804,  -1859,
   -1873,  -1848,  -1784,  -1684,
   -1550,  -1387,  -1199,   -990,
    -766,   -532,   -294,    -58,
     173,    391,    593,    773,
     929,   1057,   1154,   1218,
    1249,   1245,   1209,   1139,
    1039,    910,    757,    581,
     388,    181,    -36,   -257,
    -478,   -694,   -902,  -1098,
   -1277,  -1437,  -1574,  -1687,
   -1774,  -1834,  -1867,  -1872,
   -1852,  -1806,  -1738,  -1648,
   -1541,  -1419,  -1286,  -1145,
    -999,   -852,   -709,   -571,
    -442,   -326,   -224,   -139,
     -72,    -25,      1,      7,
      -7,    -42,    -95,   -166,
    -252,   -352,   -463,   -583,
    -708,   -838,   -968,  -1096,
   -1221,  -1339,  -1448,  -1547,
   -1635,  -1710,  -1771,  -1818,
   -1851,  -1870,  -1876,  -1869,
   -1851,  -1822,  -1785,  -1740,
   -1691,  -1637,  -1582,  -1526,
   -1472,  -1421,  -1373,  -1332,
   -1296,  -1268,  -1247,  -1234,
   -1228,  -1231,  -1241,  -1258,
   -1281,  -1309,  -1342,  -1378,
   -1417,  -1458,  -1499,  -1540,
   -1580,  -1618,  -1654,  -1687,
   -1718,  -1745,  -1770,  -1791,
   -1811,  -1828,  -1844,  -1859,
   -1170,  -1183,  -1194,  -1204,
   -1214,  -1106,   -888,   -571,
    -173,    287,    786,   1298,
    1798,   2262,   2666,   2992,
    3223,   3350,   3365,   3269,
    3068,   2770,   2391,   1950,
    1467,    967,    472,      8,
    -406,   -749,  -1006,  -1166,
   -1222,  -1174,  -1024,   -781,
    -459,    -73,    355,    805,
    1254,   1680,   2063,   2382,
    2624,   2777,   2833,   2791,
    2653,   2425,   2121,   1753,
    1341,    904,    464,     41,
    -346,   -677,   -939,  -1119,
   -1210,  -1209,  -1118,   -942,
    -691,   -378,    -20,    365,
     758,   1139,   1489,   1792,
    2032,   2199,   2284,   2284,
    2199,   2035,   1798,   1502,
    1160,    789,    407,     32,
    -318,   -627,   -881,  -1069,
   -1183,  -1219,  -1176,  -1058,
    -872,   -629,   -340,    -21,
     312,    641,    951,   1227,
    1454,   1623,   1725,   1756,
    1714,   1603,   1428,   1197,
     923,    618,    298,    -23,
    -329,   -606,   -842,  -1026,
   -1151,  -1212,  -1207,  -1138,
   -1009,   -828,   -605,   -352,
     -82,    191,    454,    693,
     898,   1057,   1164,   1214,
    1204,   1136,   1014,    844,
     633,    394,    136,   -126,
    -382,   -620,   -828,   -997,
   -1121,  -1195,  -1216,  -1185,
   -1105,   -980,   -819,   -630,
    -423,   -209,      2,    197,
     369,    508,    609,    666,
     677,    642,    563,    445,
     294,    116,    -79,   -282,
    -483,   -673,   -844,   -989,
   -1101,  -1176,  -1212,  -1208,
   -1166,  -1090,   -984,   -855,
    -710,   -556,   -402,   -256,
    -125,    -16,     67,    120,
     140,    127,     81,      7,
     -93,   -213,   -347,   -490,
    -633,   -771,   -898,  -1008,
   -1098,  -1163,  -1202,  -1214,
   -1200,  -1163,  -1105,  -1031,
    -944,   -850,   -755,   -664,
    -580,   -509,   -454,   -417,
    -400,   -402,   -425,   -465,
    -521,   -590,   -667,   -750,
    -835,   -917,   -994,  -1061,
   -1118,  -1163,  -1193,  -1210,
   -1214,  -1205,  -1187,  -1160,
   -1128,  -1092,  -1056,  -1022,
    -991,   -966,   -947,   -936,
    -933,   -937,   -948,   -965,
    -986,  -1010,  -1037,  -1063,
   -1089,  -1113,  -1135,  -1154,
   -1170,  -1183,  -1194,  -1204,
    -864,   -876,   -885,   -893,
    -900,   -753,   -467,    -68,
     409,    921,   1424,   1873,
    2230,   2465,   2558,   2501,
    2300,   1973,   1548,   1061,
     556,     73,   -345,   -664,
    -859,   -914,   -826,   -605,
    -271,    146,    607,   1074,
    1504,   1862,   2116,   2245,
    2238,   2096,   1833,   1471,
    1042,    582,    130,   -274,
    -598,   -816,   -910,   -873,
    -712,   -441,    -85,    324,
     749,   1153,   1502,   1765,
    1921,   1955,   1866,   1662,
    1361,    990,    579,    165,
    -218,   -539,   -770,   -893,
    -900,   -792,   -579,   -283,
      71,    451,    823,   1155,
    1418,   1590,   1657,   1613,
    1463,   1220,    906,    547,
     174,   -181,   -489,   -724,
    -867,   -909,   -847,   -689,
    -449,   -150,    181,    515,
     823,   1078,   1258,   1348,
    1341,   1238,   1049,    790,
     483,    156,   -165,   -452,
    -683,   -838,   -905,   -882,
    -771,   -585,   -339,    -58,
     234,    511,    750,    929,
    1033,   1054,    991,    850,
     643,    389,    109,   -173,
    -434,   -651,   -808,   -893,
    -900,   -830,   -692,   -498,
    -267,    -20,    222,    437,
     606,    715,    756,    725,
     626,    468,    264,     32,
    -208,   -435,   -633,   -783,
    -876,   -905,   -869,   -773,
    -627,   -446,   -245,    -43,
     142,    294,    400,    452,
     445,    380,    265,    109,
     -75,   -270,   -461,   -631,
    -767,   -859,   -901,   -891,
    -831,   -729,   -594,   -440,
    -281,   -131,     -3,     92,
     145,    153,    116,     38,
     -75,   -212,   -362,   -511,
    -649,   -764,   -847,   -893,
    -900,   -869,   -804,   -713,
    -605,   -490,   -379,   -282,
    -206,   -159,   -145,   -162,
    -211,   -285,   -378,   -483,
    -590,   -690,   -776,   -843,
    -885,   -901,   -890,   -857,
    -806,   -741,   -671,   -601,
    -539,   -490,   -458,   -445,
    -452,   -477,   -519,   -573,
    -633,   -696,   -756,   -809,
    -851,   -881,   -897,   -899,
    -891,   -873,   -848,   -822,
    -795,   -773,   -755,   -745,
    -743,   -747,   -759,   -774,
    -793,   -813,   -832,   -850,
    -864,   -876,   -885,   -893,
    -779,   -780,   -784,   -789,
    -795,   -630,   -312,    121,
     622,   1134,   1601,   1973,
    2209,   2284,   2191,   1940,
    1559,   1090,    583,     94,
    -325,   -631,   -792,   -792,
    -634,   -336,     68,    531,
    1003,   1432,   1771,   1984,
    2047,   1955,   1718,   1362,
     927,    460,     10,   -374,
    -652,   -795,   -790,   -639,
    -362,     11,    438,    870,
    1261,   1568,   1758,   1810,
    1719,   1497,   1168,    767,
     339,    -72,   -420,   -670,
    -797,   -788,   -646,   -390,
     -47,    342,    735,   1088,
    1363,   1530,   1572,   1485,
    1278,    976,    610,    221,
    -150,   -464,   -687,   -798,
    -786,   -654,   -420,   -109,
     243,    596,    912,   1156,
    1302,   1335,   1251,   1062,
     786,    456,    106,   -227,
    -506,   -703,   -799,   -784,
    -664,   -452,   -173,    141,
     454,    733,    947,   1073,
    1097,   1019,    846,    599,
     304,     -7,   -300,   -545,
    -717,   -799,   -784,   -675,
    -486,   -240,     36,    310,
     552,    736,    843,    860,
     787,    633,    415,    156,
    -116,   -371,   -583,   -730,
    -799,   -783,   -687,   -523,
    -309,    -72,    163,    369,
     524,    612,    623,    557,
     422,    233,     10,   -222,
    -439,   -618,   -742,   -799,
    -784,   -701,   -561,   -382,
    -183,     12,    183,    310,
     380,    386,    328,    212,
      53,   -133,   -326,   -505,
    -652,   -753,   -798,   -785,
    -716,   -602,   -457,   -297,
    -140,     -5,     94,    147,
     149,     99,      5,   -124,
    -273,   -426,   -568,   -683,
    -762,   -797,   -786,   -733,
    -646,   -535,   -413,   -296,
    -195,   -123,    -86,    -88,
    -128,   -201,   -298,   -410,
    -524,   -628,   -713,   -770,
    -796,   -789,   -752,   -692,
    -615,   -533,   -454,   -388,
    -342,   -320,   -324,   -353,
    -404,   -470,   -544,   -619,
    -686,   -740,   -777,   -794,
    -792,   -772,   -740,   -699,
    -655,   -615,   -583,   -562,
    -554,   -560,   -578,   -605,
    -639,   -675,   -710,   -741,
    -766,   -783,   -793,   -796,
    -795,   -790,   -785,   -781,
    -779,   -780,   -784,   -789,
    -681,   -692,   -700,   -707,
    -712,   -528,   -182,    279,
     791,   1285,   1694,   1963,
    2057,   1965,   1698,   1294,
     806,    301,   -156,   -505,
    -700,   -717,   -557,   -244,
     180,    656,   1119,   1507,
    1767,   1866,   1791,   1552,
    1183,    733,    261,   -169,
    -501,   -693,   -721,   -584,
    -301,     87,    526,    957,
    1322,   1572,   1674,   1615,
    1403,   1068,    654,    218,
    -185,   -500,   -687,   -723,
    -607,   -355,     -3,    401,
     800,   1141,   1379,   1482,
    1437,   1250,    948,    571,
     169,   -204,   -500,   -681,
    -725,   -627,   -404,    -87,
     280,    646,    963,   1187,
    1289,   1257,   1094,    824,
     483,    116,   -227,   -503,
    -676,   -725,   -645,   -450,
    -167,    164,    497,    788,
     997,   1097,   1075,    935,
     696,    390,     59,   -254,
    -509,   -672,   -724,   -660,
    -492,   -242,     52,    352,
     616,    808,    904,    891,
     772,    563,    293,     -3,
    -285,   -517,   -669,   -723,
    -673,   -530,   -313,    -54,
     211,    447,    622,    712,
     707,    607,    427,    191,
     -70,   -320,   -528,   -667,
    -721,   -684,   -564,   -380,
    -156,     75,    282,    437,
     520,    520,    438,    286,
      84,   -141,   -359,   -541,
    -666,   -718,   -693,   -596,
    -442,   -253,    -57,    121,
     255,    329,    333,    267,
     141,    -28,   -217,   -402,
    -558,   -667,   -716,   -700,
    -624,   -499,   -346,   -184,
     -37,     75,    139,    145,
      94,     -7,   -143,   -297,
    -449,   -578,   -670,   -713,
    -705,   -648,   -553,   -433,
    -307,   -191,   -102,    -51,
     -44,    -82,   -159,   -264,
    -383,   -500,   -601,   -674,
    -711,   -709,   -670,   -602,
    -516,   -425,   -341,   -276,
    -239,   -234,   -260,   -315,
    -389,   -473,   -556,   -628,
    -681,   -709,   -711,   -689,
    -648,   -595,   -539,   -487,
    -448,   -426,   -424,   -441,
    -474,   -518,   -568,   -616,
    -658,   -689,   -707,   -712,
    -705,   -689,   -669,   -647,
    -629,   -617,   -612,   -614,
    -623,   -636,   -652,   -667,
    -681,   -692,   -700,   -707,
    -410,   -419,   -426,   -431,
    -434,   -147,    331,    836,
    1198,   1295,   1096,    668,
     156,   -269,   -465,   -371,
     -20,    465,    920,   1192,
    1188,    913,    458,    -22,
    -368,   -465,   -285,    109,
     582,    972,   1149,   1054,
     720,    260,   -171,   -431,
    -434,   -184,    234,    675,
     990,   1075,    900,    527,
      80,   -290,   -461,   -379,
     -75,    346,    740,    975,
     972,    733,    339,    -77,
    -376,   -461,   -305,     34,
     441,    777,    929,    846,
     559,    163,   -208,   -431,
    -434,   -220,    136,    513,
     783,    854,    705,    386,
       5,   -310,   -457,   -388,
    -130,    227,    561,    759,
     756,    553,    220,   -132,
    -385,   -456,   -326,    -41,
     300,    581,    708,    639,
     397,     66,   -244,   -431,
    -434,   -257,     39,    352,
     575,    633,    509,    245,
     -70,   -331,   -452,   -396,
    -185,    107,    381,    543,
     539,    373,    100,   -187,
    -393,   -452,   -347,   -117,
     159,    386,    487,    431,
     236,    -31,   -281,   -431,
    -434,   -293,    -58,    190,
     367,    413,    314,    104,
    -146,   -352,   -448,   -405,
    -240,    -12,    201,    326,
     323,    193,    -19,   -241,
    -401,   -448,   -368,   -192,
      18,    190,    267,    223,
      74,   -128,   -317,   -431,
    -434,   -330,   -155,     29,
     159,    192,    118,    -37,
    -221,   -373,   -444,   -413,
    -295,   -131,     21,    110,
     106,     13,   -138,   -296,
    -410,   -443,   -389,   -268,
    -123,     -6,     46,     15,
     -87,   -225,   -354,   -431,
    -434,   -366,   -252,   -133,
     -49,    -29,    -78,   -178,
    -296,   -394,   -439,   -422,
    -349,   -250,   -159,   -106,
    -110,   -167,   -257,   -351,
    -418,   -439,   -409,   -343,
    -264,   -201,   -175,   -193,
    -248,   -322,   -390,   -431,
    -434,   -402,   -349,   -294,
    -257,   -249,   -273,   -319,
    -372,   -414,   -435,   -430,
    -404,   -370,   -339,   -323,
    -326,   -347,   -377,   -406,
    -427,   -435,   -430,   -418,
    -405,   -397,   -395,   -401,
    -410,   -419,   -426,   -431,
   -5085,  -5094,  -5107,  -5123,
   -5164,  -5158,  -5105,  -5008,
   -4867,  -4685,  -4464,  -4204,
   -3910,  -3583,  -3226,  -2840,
   -2430,  -1997,  -1544,  -1075,
    -591,    -96,    407,    916,
    1428,   1940,   2449,   2954,
    3451,   3938,   4413,   4874,
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    1168,    798,    316,    -45,
    -136,     35,    315,    504,
     477,    253,    -19,   -156,
     -52,    263,    640,    898,
     928,    749,    488,    301,
     278,    400,    556,    617,
     514,    279,     23,   -131,
    -117,     40,    244,    390,
     424,    362,    279,    252,
     315,    440,    558,    602,
     547,    420,    278,    178,
     142,    151,    169,    165,
     134,     97,     83,    108,
     165,    231,    282,    311,
     324,    336,    354,    367,
     357,    313,    238,    159,
     106,     96,    118,    143,
     139,     97,     37,      0,
      21,    107,    223,    315,
     337,    281,    184,    105,
      91,    146,    229,    276,
     240,    123,    -23,   -124,
    -127,    -34,    101,    199,
     207,    126,     10,    -60,
     -34,     81,    222,    308,
     283,    156,     -7,   -120,
    -129,    -39,     85,    159,
     133,     16,   -124,   -204,
    -175,    -49,    104,    201,
     191,     85,    -51,   -137,
    -124,    -27,     91,    151,
     112,    -12,   -155,   -241,
    -227,   -128,     -7,     65,
      49,    -41,   -147,   -204,
    -176,    -80,     28,     83,
      55,    -41,   -152,   -218,
    -211,   -144,    -66,    -27,
     -55,   -133,   -217,   -258,
    -236,   -165,    -88,    -46,
     -61,   -119,   -184,   -218,
    -206,   -162,   -116,   -100,
    -126,   -181,   -237,   -267,
    -259,   -226,   -191,   -176,
    -187,   -216,   -244,   -254,
    -242,   -218,   -197,   -193,
    -206,   -229,   -251,   -263,
    -264,   -261,   -262,   -269,
    -280,   -290,   -294,   -293,
    -290,   -290,   -295,   -301,
    -303,   -299,   -291,   -285,
    -289,   -304,   -324,   -342,
    -348,   -341,   -329,   -323,
    -330,   -352,   -377,   -394,
    -392,   -374,   -350,   -336,
    -342,   -366,   -395,   -414,
    -412,   -393,   -370,   -360,
    -372,   -403,   -437,   -458,
    -456,   -435,   -410,   -398,
    -408,   -435,   -465,   -481,
    -476,   -456,   -433,   -424,
    -434,   -459,   -484,   -497,
   -6397,  -6430,  -6465,  -6503,
   -6557,  -6386,  -6071,  -5675,
   -5230,  -4758,  -4267,  -3766,
   -3259,  -2748,  -2236,  -1724,
   -1214,   -707,   -203,    298,
     794,   1286,   1772,   2254,
    2730,   3201,   3666,   4124,
    4577,   5024,   5464,   5898,
    6324,   6744,   7156,   7559,
    7954,   8339,   8711,   9069,
    9405,   9706,   9949,  10127,
   10263,  10373,  10466,  10547,
   10615,  10671,  10714,  10741,
   10744,  10714,  10637,  10514,
   10354,  10164,   9940,   9677,
    9376,   9047,   8701,   8346,
    7986,   7624,   7260,   6897,
    6535,   6175,   5817,   5462,
    5111,   4763,   4420,   4083,
    3752,   3429,   3119,   2830,
    2576,   2368,   2193,   2035,
    1888,   1748,   1613,   1481,
    1353,   1228,   1105,    985,
     867,    752,    638,    527,
     419,    313,    211,    111,
      17,    -72,   -152,   -219,
    -268,   -299,   -318,   -329,
    -335,   -336,   -333,   -325,
    -308,   -279,   -233,   -168,
     -94,    -20,     39,     71,
      81,     79,     71,     60,
      46,     31,     15,     -3,
     -21,    -40,    -60,    -80,
    -101,   -123,   -146,   -168,
    -192,   -216,   -241,   -266,
    -291,   -318,   -344,   -372,
    -400,   -428,   -457,   -487,
    -517,   -548,   -580,   -613,
    -649,   -687,   -730,   -773,
    -809,   -828,   -830,   -824,
    -814,   -802,   -791,   -780,
    -771,   -764,   -761,   -763,
    -773,   -795,   -831,   -877,
    -931,   -988,  -1048,  -1110,
   -1174,  -1238,  -1303,  -1368,
   -1434,  -1500,  -1566,  -1632,
   -1699,  -1766,  -1833,  -1900,
   -1968,  -2037,  -2106,  -2177,
   -2249,  -2326,  -2409,  -2504,
   -2613,  -2729,  -2848,  -2969,
   -3089,  -3209,  -3328,  -3445,
   -3558,  -3667,  -3775,  -3880,
   -3985,  -4088,  -4191,  -4292,
   -4393,  -4493,  -4592,  -4690,
   -4787,  -4883,  -4978,  -5071,
   -5162,  -5251,  -5337,  -5418,
   -5493,  -5560,  -5620,  -5676,
   -5728,  -5778,  -5826,  -5871,
   -5912,  -5945,  -5969,  -5988,
   -6003,  -6018,  -6032,  -6046,
   -6061,  -6075,  -6090,  -6106,
   -6122,  -6139,  -6157,  -6176,
   -6195,  -6215,  -6237,  -6259,
   -6283,  -6309,  -6336,  -6366,
   -6397,  -6430,  -6465,  -6503,
   -2674,  -2708,  -2733,  -2754,
   -2775,  -2441,  -1999,  -1516,
   -1015,   -505,      7,    518,
    1026,   1528,   2024,   2509,
    2980,   3426,   3804,   3996,
    4014,   3932,   3822,   3699,
    3569,   3434,   3297,   3157,
    3016,   2875,   2734,   2597,
    2477,   2444,   2482,   2508,
    2586,   2692,   2799,   2904,
    3008,   3110,   3209,   3306,
    3399,   3486,   3559,   3590,
    3502,   3373,   3224,   3035,
    2742,   2410,   2070,   1728,
    1389,   1053,    723,    400,
      88,   -199,   -401,   -523,
    -616,   -679,   -688,   -612,
    -425,   -201,     35,    274,
     513,    750,    982,   1203,
    1389,   1483,   1547,   1601,
    1648,   1687,   1712,   1692,
    1599,   1486,   1367,   1246,
    1127,   1011,    908,    867,
     878,    898,    920,    939,
     950,    944,    923,    936,
     998,   1070,   1142,   1212,
    1275,   1311,   1278,   1224,
    1165,   1103,   1040,    975,
     909,    839,    757,    628,
     461,    288,    116,    -44,
    -154,   -224,   -284,   -339,
    -391,   -440,   -483,   -520,
    -541,   -543,   -524,   -455,
    -359,   -262,   -183,   -156,
    -143,   -135,   -129,   -124,
    -120,   -117,   -115,   -114,
    -115,   -121,   -139,   -198,
    -267,   -304,   -313,   -318,
    -321,   -325,   -328,   -332,
    -337,   -344,   -354,   -371,
    -396,   -423,   -443,   -441,
    -467,   -501,   -536,   -572,
    -608,   -644,   -680,   -716,
    -751,   -787,   -822,   -856,
    -890,   -921,   -939,   -967,
    -998,  -1031,  -1063,  -1095,
   -1127,  -1159,  -1190,  -1220,
   -1250,  -1278,  -1304,  -1326,
   -1356,  -1408,  -1452,  -1473,
   -1489,  -1503,  -1516,  -1530,
   -1543,  -1555,  -1568,  -1580,
   -1592,  -1603,  -1609,  -1594,
   -1567,  -1541,  -1532,  -1539,
   -1551,  -1564,  -1578,  -1593,
   -1608,  -1624,  -1641,  -1660,
   -1682,  -1715,  -1770,  -1832,
   -1895,  -1953,  -1996,  -2027,
   -2055,  -2082,  -2108,  -2134,
   -2159,  -2184,  -2207,  -2226,
   -2231,  -2226,  -2220,  -2214,
   -2209,  -2209,  -2223,  -2244,
   -2267,  -2290,  -2314,  -2339,
   -2364,  -2390,  -2422,  -2465,
   -2510,  -2553,  -2595,  -2636,
   -2674,  -2708,  -2733,  -2754,
   -1833,  -1850,  -1853,  -1854,
   -1868,  -1479,  -1005,   -503,
       7,    519,   1028,   1528,
    2012,   2455,   2675,   2639,
    2543,   2431,   2312,   2190,
    2066,   1943,   1828,   1751,
    1855,   2074,   2363,   2556,
    2696,   2816,   2925,   3025,
    3109,   3125,   2987,   2796,
    2452,   2066,   1674,   1284,
     898,    522,    166,    -82,
    -227,   -340,   -367,   -272,
    -137,     64,    331,    614,
     885,   1031,   1125,   1204,
    1257,   1185,   1073,    954,
     835,    721,    636,    676,
     741,    814,    896,   1031,
    1259,   1494,   1718,   1908,
    1997,   1952,   1881,   1800,
    1711,   1603,   1397,   1156,
     913,    680,    521,    429,
     348,    272,    201,    140,
     120,    185,    262,    330,
     314,    276,    259,    272,
     296,    319,    332,    269,
     176,     99,    107,    133,
     161,    191,    221,    253,
     289,    351,    480,    585,
     621,    646,    666,    680,
     681,    657,    615,    561,
     450,    359,    307,    259,
     212,    166,    122,     77,
      34,     -6,    -35,    -65,
    -105,   -146,   -185,   -224,
    -262,   -297,   -327,   -344,
    -337,   -311,   -301,   -293,
    -285,   -277,   -270,   -264,
    -258,   -256,   -274,   -326,
    -332,   -331,   -327,   -324,
    -320,   -316,   -312,   -304,
    -264,   -204,   -189,   -207,
    -232,   -260,   -288,   -318,
    -350,   -388,   -469,   -562,
    -645,   -686,   -717,   -745,
    -773,   -798,   -821,   -833,
    -804,   -768,   -734,   -724,
    -735,   -742,   -748,   -754,
    -763,   -789,   -846,   -907,
    -967,  -1018,  -1035,  -1043,
   -1049,  -1053,  -1053,  -1028,
    -985,   -940,   -896,   -856,
    -836,   -840,   -849,   -866,
    -891,   -947,  -1013,  -1079,
   -1145,  -1210,  -1268,  -1298,
   -1320,  -1339,  -1350,  -1334,
   -1313,  -1292,  -1270,  -1250,
   -1233,  -1229,  -1244,  -1264,
   -1294,  -1343,  -1391,  -1438,
   -1484,  -1529,  -1573,  -1612,
   -1629,  -1639,  -1631,  -1612,
   -1592,  -1572,  -1553,  -1534,
   -1517,  -1502,  -1497,  -1509,
   -1540,  -1576,  -1613,  -1650,
   -1688,  -1727,  -1765,  -1801,
   -1833,  -1850,  -1853,  -1854,
   -1889,  -1885,  -1882,  -1883,
   -1898,  -1519,  -1050,   -551,
     -42,    470,    980,   1486,
    1985,   2473,   2942,   3345,
    3571,   3752,   3910,   4044,
    4133,   4080,   3779,   3376,
    2949,   2519,   2114,   1851,
    1657,   1477,   1304,   1136,
     973,    815,    661,    514,
     377,    253,    142,     67,
     110,    192,    287,    387,
     489,    593,    698,    804,
     917,   1061,   1329,   1625,
    1921,   2208,   2474,   2676,
    2771,   2776,   2704,   2604,
    2480,   2260,   1975,   1679,
    1383,   1087,    794,    505,
     222,    -53,   -316,   -552,
    -697,   -659,   -560,   -389,
    -180,     40,    262,    485,
     705,    921,   1129,   1316,
    1406,   1462,   1507,   1543,
    1566,   1554,   1470,   1359,
    1219,   1035,    844,    706,
     627,    557,    491,    426,
     364,    302,    242,    184,
     128,     76,     25,    -40,
     -98,   -145,   -165,   -157,
    -140,   -120,    -98,    -75,
     -48,    -11,     89,    217,
     348,    476,    598,    698,
     746,    771,    785,    787,
     757,    679,    544,    400,
     254,    107,    -39,   -183,
    -325,   -464,   -597,   -721,
    -813,   -806,   -764,   -711,
    -653,   -584,   -497,   -403,
    -309,   -215,   -125,    -42,
      -1,     10,     15,     16,
      11,     -5,    -58,   -128,
    -203,   -279,   -355,   -423,
    -459,   -492,   -522,   -552,
    -582,   -611,   -640,   -668,
    -695,   -722,   -747,   -781,
    -813,   -843,   -870,   -897,
    -919,   -933,   -939,   -944,
    -946,   -945,   -920,   -871,
    -818,   -766,   -717,   -675,
    -657,   -655,   -658,   -664,
    -674,   -695,   -752,   -822,
    -896,   -971,  -1046,  -1120,
   -1194,  -1266,  -1335,  -1401,
   -1457,  -1469,  -1454,  -1433,
   -1410,  -1386,  -1362,  -1336,
   -1308,  -1276,  -1245,  -1216,
   -1199,  -1204,  -1213,  -1224,
   -1237,  -1254,  -1284,  -1327,
   -1373,  -1419,  -1464,  -1504,
   -1523,  -1538,  -1555,  -1573,
   -1592,  -1610,  -1629,  -1647,
   -1665,  -1683,  -1700,  -1721,
   -1741,  -1761,  -1780,  -1798,
   -1816,  -1834,  -1851,  -1867,
   -1881,  -1892,  -1899,  -1895,
   -1889,  -1885,  -1882,  -1883,
   -5622,  -5649,  -5676,  -5705,
   -5749,  -5433,  -5018,  -4559,
   -4076,  -3577,  -3070,  -2558,
   -2046,  -1537,  -1032,   -537,
     -57,    393,    757,    862,
     740,    524,    283,     35,
    -215,   -465,   -712,   -955,
   -1192,  -1423,  -1643,  -1849,
   -2022,  -2075,  -1975,  -1785,
   -1453,  -1077,   -691,   -301,
      87,    472,    853,   1228,
    1595,   1953,   2293,   2590,
    2750,   2846,   2907,   2881,
    2755,   2606,   2448,   2289,
    2129,   1971,   1816,   1666,
    1523,   1396,   1332,   1361,
    1415,   1483,   1579,   1770,
    2017,   2276,   2537,   2797,
    3054,   3308,   3555,   3793,
    4007,   4141,   4233,   4311,
    4381,   4439,   4459,   4389,
    4287,   4177,   4064,   3951,
    3839,   3730,   3630,   3562,
    3555,   3562,   3574,   3589,
    3609,   3640,   3717,   3861,
    4020,   4182,   4343,   4500,
    4651,   4788,   4878,   4937,
    4987,   5031,   5069,   5101,
    5122,   5124,   5061,   4949,
    4819,   4678,   4527,   4370,
    4221,   4102,   3988,   3873,
    3756,   3638,   3519,   3401,
    3288,   3194,   3158,   3143,
    3132,   3121,   3104,   3062,
    3000,   2934,   2866,   2798,
    2728,   2658,   2586,   2512,
    2430,   2322,   2168,   2003,
    1837,   1680,   1545,   1419,
    1294,   1171,   1049,    927,
     807,    689,    572,    459,
     355,    285,    245,    209,
     162,    104,     43,    -18,
     -79,   -140,   -201,   -262,
    -323,   -385,   -448,   -514,
    -590,   -702,   -824,   -937,
   -1045,  -1153,  -1259,  -1366,
   -1471,  -1577,  -1681,  -1784,
   -1887,  -1988,  -2088,  -2183,
   -2264,  -2322,  -2378,  -2434,
   -2489,  -2543,  -2597,  -2650,
   -2703,  -2756,  -2809,  -2861,
   -2914,  -2967,  -3021,  -3077,
   -3144,  -3228,  -3316,  -3404,
   -3492,  -3580,  -3668,  -3755,
   -3841,  -3927,  -4011,  -4095,
   -4178,  -4259,  -4341,  -4422,
   -4481,  -4529,  -4573,  -4614,
   -4653,  -4690,  -4724,  -4755,
   -4783,  -4808,  -4831,  -4851,
   -4869,  -4883,  -4897,  -4916,
   -4953,  -4994,  -5036,  -5079,
   -5122,  -5165,  -5208,  -5250,
   -5293,  -5336,  -5379,  -5423,
   -5469,  -5515,  -5559,  -5595,
   -5622,  -5649,  -5676,  -5705,
   -1547,  -1557,  -1568,  -1579,
   -1591,  -1184,   -700,   -195,
     317,    828,   1335,   1832,
    2310,   2702,   2908,   3069,
    3140,   3005,   2822,   2624,
    2414,   2177,   1872,   1682,
    1509,   1341,   1178,   1027,
     911,    953,   1058,   1152,
    1090,    981,    865,    749,
     634,    524,    426,    370,
     414,    530,    631,    729,
     826,    924,   1022,   1119,
    1212,   1296,   1309,   1216,
    1117,   1052,   1094,   1156,
    1209,   1214,   1147,   1094,
    1157,   1234,   1310,   1383,
    1449,   1496,   1456,   1369,
    1253,   1015,    753,    488,
     228,    -24,   -254,   -419,
    -520,   -582,   -496,   -303,
     -92,    123,    339,    554,
     765,    971,   1164,   1288,
    1342,   1378,   1390,   1333,
    1239,   1082,    892,    700,
     541,    466,    402,    342,
     284,    230,    185,    180,
     198,    202,    122,     29,
     -64,   -149,   -210,   -217,
    -204,   -183,   -152,    -65,
      12,     86,    159,    231,
     302,    372,    438,    497,
     497,    460,    416,    371,
     330,    257,    174,     91,
      11,    -36,    -30,    -19,
      -6,      6,     16,     22,
       6,    -29,    -83,   -195,
    -312,   -420,   -496,   -544,
    -583,   -617,   -646,   -662,
    -612,   -530,   -441,   -352,
    -263,   -175,    -90,     -8,
      66,     92,     92,     77,
      25,    -61,   -156,   -254,
    -351,   -444,   -507,   -539,
    -567,   -593,   -617,   -641,
    -662,   -674,   -678,   -696,
    -747,   -789,   -806,   -813,
    -818,   -821,   -823,   -823,
    -815,   -773,   -735,   -698,
    -662,   -626,   -592,   -559,
    -528,   -505,   -520,   -560,
    -621,   -686,   -744,   -800,
    -854,   -907,   -957,   -982,
    -991,   -997,  -1002,  -1008,
   -1013,  -1020,  -1031,  -1047,
   -1073,  -1106,  -1129,  -1149,
   -1168,  -1187,  -1204,  -1221,
   -1236,  -1243,  -1224,  -1196,
   -1167,  -1139,  -1111,  -1083,
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   -5280,  -5414,  -5548,  -5681,
   -5815,  -5949,  -6082,  -6216,
   -6350,  -6483,  -6617,  -6751,
   -6884,  -7018,  -7152,  -7285,
   -7419,  -7553,  -7686,  -7820,
   -7954,  -8087,  -8221,  -8355,
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   -9558,  -9691,  -9825,  -9959,
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  -10627, -10761, -10895, -11028,
  -11162, -11296, -11429, -11563,
  -11697, -11830, -11964, -12098,
  -12231, -12365, -12499, -12632,
  -12766, -12900, -13033, -13167,
  -13301, -13434, -13568, -13056,
   -8296,  -8372,  -8448,  -7936,
   -7424,  -6912,  -6400,  -5888,
   -5376,  -4864,  -4352,  -3840,
   -3328,  -2816,  -2304,  -1792,
   -1280,   -768,   -256,    256,
     768,   1280,   1792,   2304,
    2816,   3328,   3840,   4352,
    4864,   5376,   5888,   6400,
    6912,   7424,   7936,   8448,
    8372,   8296,   8221,   8145,
    8069,   7993,   7918,   7842,
    7766,   7690,   7615,   7539,
    7463,   7387,   7311,   7236,
    7160,   7084,   7008,   6933,
    6857,   6781,   6705,   6630,
    6554,   6478,   6402,   6327,
    6251,   6175,   6099,   6023,
    5948,   5872,   5796,   5720,
    5645,   5569,   5493,   5417,
    5342,   5266,   5190,   5114,
    5038,   4963,   4887,   4811,
    4735,   4660,   4584,   4508,
    4432,   4357,   4281,   4205,
    4129,   4054,   3978,   3902,
    3826,   3750,   3675,   3599,
    3523,   3447,   3372,   3296,
    3220,   3144,   3069,   2993,
    2917,   2841,   2765,   2690,
    2614,   2538,   2462,   2387,
    2311,   2235,   2159,   2084,
    2008,   1932,   1856,   1781,
    1705,   1629,   1553,   1477,
    1402,   1326,   1250,   1174,
    1099,   1023,    947,    871,
     796,    720,    644,    568,
     492,    417,    341,    265,
     189,    114,     38,    -38,
    -114,   -189,   -265,   -341,
    -417,   -492,   -568,   -644,
    -720,   -796,   -871,   -947,
   -1023,  -1099,  -1174,  -1250,
   -1326,  -1402,  -1477,  -1553,
   -1629,  -1705,  -1781,  -1856,
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   -2538,  -2614,  -2690,  -2765,
   -2841,  -2917,  -2993,  -3069,
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   -3447,  -3523,  -3599,  -3675,
   -3750,  -3826,  -3902,  -3978,
   -4054,  -4129,  -4205,  -4281,
   -4357,  -4432,  -4508,  -4584,
   -4660,  -4735,  -4811,  -4887,
   -4963,  -5038,  -5114,  -5190,
   -5266,  -5342,  -5417,  -5493,
   -5569,  -5645,  -5720,  -5796,
   -5872,  -5948,  -6023,  -6099,
   -6175,  -6251,  -6327,  -6402,
   -6478,  -6554,  -6630,  -6705,
   -6781,  -6857,  -6933,  -7008,
   -7084,  -7160,  -7236,  -7311,
   -7387,  -7463,  -7539,  -7615,
   -7690,  -7766,  -7842,  -7918,
   -7993,  -8069,  -8145,  -8221,
   -8296,  -8372,  -8448,  -7936,
   -4279,  -4316,  -4352,  -3840,
   -3328,  -2816,  -2304,  -1792,
   -1280,   -768,   -256,    256,
     768,   1280,   1792,   2304,
    2816,   3328,   3840,   4352,
    4316,   4279,   4243,   4206,
    4170,   4133,   4097,   4061,
    4024,   3988,   3951,   3915,
    3879,   3842,   3806,   3769,
    3733,   3696,   3660,   3624,
    3587,   3551,   3514,   3478,
    3442,   3405,   3369,   3332,
    3296,   3259,   3223,   3187,
    3150,   3114,   3077,   3041,
    3005,   2968,   2932,   2895,
    2859,   2822,   2786,   2750,
    2713,   2677,   2640,   2604,
    2567,   2531,   2495,   2458,
    2422,   2385,   2349,   2313,
    2276,   2240,   2203,   2167,
    2130,   2094,   2058,   2021,
    1985,   1948,   1912,   1876,
    1839,   1803,   1766,   1730,
    1693,   1657,   1621,   1584,
    1548,   1511,   1475,   1439,
    1402,   1366,   1329,   1293,
    1256,   1220,   1184,   1147,
    1111,   1074,   1038,   1002,
     965,    929,    892,    856,
     819,    783,    747,    710,
     674,    637,    601,    564,
     528,    492,    455,    419,
     382,    346,    310,    273,
     237,    200,    164,    127,
      91,     55,     18,    -18,
     -55,    -91,   -127,   -164,
    -200,   -237,   -273,   -310,
    -346,   -382,   -419,   -455,
    -492,   -528,   -564,   -601,
    -637,   -674,   -710,   -747,
    -783,   -819,   -856,   -892,
    -929,   -965,  -1002,  -1038,
   -1074,  -1111,  -1147,  -1184,
   -1220,  -1256,  -1293,  -1329,
   -1366,  -1402,  -1439,  -1475,
   -1511,  -1548,  -1584,  -1621,
   -1657,  -1693,  -1730,  -1766,
   -1803,  -1839,  -1876,  -1912,
   -1948,  -1985,  -2021,  -2058,
   -2094,  -2130,  -2167,  -2203,
   -2240,  -2276,  -2313,  -2349,
   -2385,  -2422,  -2458,  -2495,
   -2531,  -2567,  -2604,  -2640,
   -2677,  -2713,  -2750,  -2786,
   -2822,  -2859,  -2895,  -2932,
   -2968,  -3005,  -3041,  -3077,
   -3114,  -3150,  -3187,  -3223,
   -3259,  -3296,  -3332,  -3369,
   -3405,  -3442,  -3478,  -3514,
   -3551,  -3587,  -3624,  -3660,
   -3696,  -3733,  -3769,  -3806,
   -3842,  -3879,  -3915,  -3951,
   -3988,  -4024,  -4061,  -4097,
   -4133,  -4170,  -4206,  -4243,
   -4279,  -4316,  -4352,  -3840,
   -2267,  -2285,  -2304,  -1792,
   -1280,   -768,   -256,    256,
     768,   1280,   1792,   2304,
    2285,   2267,   2248,   2229,
    2211,   2192,   2173,   2155,
    2136,   2117,   2099,   2080,
    2061,   2043,   2024,   2006,
    1987,   1968,   1950,   1931,
    1912,   1894,   1875,   1856,
    1838,   1819,   1800,   1782,
    1763,   1744,   1726,   1707,
    1688,   1670,   1651,   1632,
    1614,   1595,   1576,   1558,
    1539,   1520,   1502,   1483,
    1464,   1446,   1427,   1409,
    1390,   1371,   1353,   1334,
    1315,   1297,   1278,   1259,
    1241,   1222,   1203,   1185,
    1166,   1147,   1129,   1110,
    1091,   1073,   1054,   1035,
    1017,    998,    979,    961,
     942,    923,    905,    886,
     867,    849,    830,    812,
     793,    774,    756,    737,
     718,    700,    681,    662,
     644,    625,    606,    588,
     569,    550,    532,    513,
     494,    476,    457,    438,
     420,    401,    382,    364,
     345,    326,    308,    289,
     271,    252,    233,    215,
     196,    177,    159,    140,
     121,    103,     84,     65,
      47,     28,      9,     -9,
     -28,    -47,    -65,    -84,
    -103,   -121,   -140,   -159,
    -177,   -196,   -215,   -233,
    -252,   -271,   -289,   -308,
    -326,   -345,   -364,   -382,
    -401,   -420,   -438,   -457,
    -476,   -494,   -513,   -532,
    -550,   -569,   -588,   -606,
    -625,   -644,   -662,   -681,
    -700,   -718,   -737,   -756,
    -774,   -793,   -812,   -830,
    -849,   -867,   -886,   -905,
    -923,   -942,   -961,   -979,
    -998,  -1017,  -1035,  -1054,
   -1073,  -1091,  -1110,  -1129,
   -1147,  -1166,  -1185,  -1203,
   -1222,  -1241,  -1259,  -1278,
   -1297,  -1315,  -1334,  -1353,
   -1371,  -1390,  -1409,  -1427,
   -1446,  -1464,  -1483,  -1502,
   -1520,  -1539,  -1558,  -1576,
   -1595,  -1614,  -1632,  -1651,
   -1670,  -1688,  -1707,  -1726,
   -1744,  -1763,  -1782,  -1800,
   -1819,  -1838,  -1856,  -1875,
   -1894,  -1912,  -1931,  -1950,
   -1968,  -1987,  -2006,  -2024,
   -2043,  -2061,  -2080,  -2099,
   -2117,  -2136,  -2155,  -2173,
   -2192,  -2211,  -2229,  -2248,
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  -27286, -27178, -26970, -26670,
  -26294, -25859, -25383, -24885,
  -24380, -23881, -23397, -22931,
  -22485, -22056, -21638, -21224,
  -20807, -20382, -19944, -19490,
  -19020, -18536, -18042, -17542,
  -17041, -16543, -16051, -15567,
  -15090, -14620, -14153, -13687,
  -13217, -12742, -12259, -11768,
  -11268, -10761, -10251,  -9739,
   -9228,  -8722,  -8221,  -7726,
   -7237,  -6754,  -6272,  -5792,
   -5310,  -4825,  -4336,  -3842,
   -3345,  -2846,  -2346,  -1849,
   -1356,   -868,   -388,     85,
     552,   1013,   1471,   1926,
    2381,   2836,   3292,   3749,
    4205,   4660,   5111,   5557,
    5996,   6427,   6849,   7263,
    7669,   8068,   8462,   8851,
    9238,   9623,  10005,  10385,
   10761,  11133,  11497,  11854,
   12201,  12538,  12864,  13181,
   13488,  13787,  14079,  14365,
   14647,  14925,  15197,  15465,
   15726,  15980,  16225,  16459,
   16682,  16893,  17092,  17280,
   17458,  17627,  17788,  17943,
   18091,  18234,  18370,  18500,
   18621,  18733,  18834,  18923,
   19000,  19064,  19116,  19157,
   19187,  19208,  19222,  19228,
   19228,  19222,  19208,  19187,
   19157,  19116,  19064,  19000,
   18923,  18834,  18733,  18621,
   18500,  18370,  18234,  18091,
   17943,  17788,  17627,  17458,
   17280,  17092,  16893,  16682,
   16459,  16225,  15980,  15726,
   15465,  15197,  14925,  14647,
   14365,  14079,  13787,  13488,
   13181,  12864,  12538,  12201,
   11854,  11497,  11133,  10761,
   10385,  10005,   9623,   9238,
    8851,   8462,   8068,   7669,
    7263,   6849,   6427,   5996,
    5557,   5111,   4660,   4205,
    3749,   3292,   2836,   2381,
    1926,   1471,   1013,    552,
      85,   -388,   -868,  -1356,
   -1849,  -2346,  -2846,  -3345,
   -3842,  -4336,  -4825,  -5310,
   -5792,  -6272,  -6754,  -7237,
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  -11768, -12259, -12742, -13217,
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  -15567, -16051, -16543, -17041,
  -17542, -18042, -18536, -19020,
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  -21224, -21638, -22056, -22485,
  -22931, -23397, -23881, -24380,
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    1735,   2151,   2559,   2964,
    3368,   3773,   4179,   4587,
    4994,   5398,   5795,   6184,
    6560,   6923,   7271,   7605,
    7927,   8238,   8540,   8837,
    9129,   9418,   9704,   9986,
   10262,  10532,  10791,  11039,
   11275,  11496,  11705,  11900,
   12084,  12259,  12426,  12586,
   12741,  12891,  13037,  13177,
   13310,  13436,  13552,  13659,
   13756,  13843,  13921,  13990,
   14052,  14108,  14159,  14205,
   14248,  14288,  14324,  14357,
   14386,  14410,  14430,  14446,
   14457,  14465,  14471,  14474,
   14476,  14476,  14477,  14477,
   14477,  14477,  14476,  14476,
   14474,  14471,  14465,  14457,
   14446,  14430,  14410,  14386,
   14357,  14324,  14288,  14248,
   14205,  14159,  14108,  14052,
   13990,  13921,  13843,  13756,
   13659,  13552,  13436,  13310,
   13177,  13037,  12891,  12741,
   12586,  12426,  12259,  12084,
   11900,  11705,  11496,  11275,
   11039,  10791,  10532,  10262,
    9986,   9704,   9418,   9129,
    8837,   8540,   8238,   7927,
    7605,   7271,   6923,   6560,
    6184,   5795,   5398,   4994,
    4587,   4179,   3773,   3368,
    2964,   2559,   2151,   1735,
    1309,    872,    421,    -43,
    -517,  -1001,  -1488,  -1975,
   -2457,  -2933,  -3401,  -3861,
   -4314,  -4765,  -5217,  -5674,
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  -11928, -12353, -12778, -13211,
  -13654, -14112, -14585, -15069,
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  -17412, -17815, -18191, -18544,
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  -22173, -22658, -23099, -23469,
  -23745, -23921, -24006, -24028,
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  -19775, -19774, -19759, -19699,
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  -17960, -17498, -17087, -16737,
  -16443, -16189, -15961, -15743,
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   -7727,  -7237,  -6730,  -6218,
   -5712,  -5222,  -4753,  -4307,
   -3882,  -3473,  -3074,  -2677,
   -2275,  -1863,  -1436,   -993,
    -538,    -75,    389,    844,
    1285,   1705,   2102,   2475,
    2829,   3167,   3493,   3813,
    4132,   4452,   4774,   5098,
    5422,   5741,   6049,   6344,
    6621,   6878,   7115,   7333,
    7535,   7724,   7902,   8074,
    8241,   8404,   8563,   8719,
    8868,   9010,   9141,   9262,
    9370,   9466,   9551,   9625,
    9691,   9751,   9805,   9856,
    9903,   9947,   9988,  10026,
   10061,  10092,  10118,  10141,
   10159,  10174,  10186,  10195,
   10202,  10209,  10214,  10218,
   10221,  10225,  10227,  10229,
   10231,  10232,  10233,  10233,
   10233,  10234,  10234,  10234,
   10234,  10234,  10234,  10234,
   10234,  10234,  10234,  10234,
   10234,  10234,  10234,  10233,
   10233,  10233,  10232,  10231,
   10229,  10227,  10225,  10221,
   10218,  10214,  10209,  10202,
   10195,  10186,  10174,  10159,
   10141,  10118,  10092,  10061,
   10026,   9988,   9947,   9903,
    9856,   9805,   9751,   9691,
    9625,   9551,   9466,   9370,
    9262,   9141,   9010,   8868,
    8719,   8563,   8404,   8241,
    8074,   7902,   7724,   7535,
    7333,   7115,   6878,   6621,
    6344,   6049,   5741,   5422,
    5098,   4774,   4452,   4132,
    3813,   3493,   3167,   2829,
    2475,   2102,   1705,   1285,
     844,    389,    -75,   -538,
    -993,  -1436,  -1863,  -2275,
   -2677,  -3074,  -3473,  -3882,
   -4307,  -4753,  -5222,  -5712,
   -6218,  -6730,  -7237,  -7727,
   -8192,  -8627,  -9032,  -9412,
   -9774, -10127, -10480, -10845,
  -11229, -11639, -12075, -12534,
  -13003, -13468, -13912, -14320,
  -14683, -15000, -15275, -15519,
  -15743, -15961, -16189, -16443,
  -16737, -17087, -17498, -17960,
  -18444, -18903, -19284, -19550,
  -19699, -19759, -19774, -19775,
  -14767, -14774, -14775, -14775,
  -14775, -14775, -14774, -14767,
  -14724, -14585, -14302, -13891,
  -13433, -13016, -12687, -12448,
  -12278, -12153, -12051, -11958,
  -11860, -11744, -11596, -11400,
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   -9580,  -9170,  -8798,  -8470,
   -8181,  -7921,  -7677,  -7434,
   -7179,  -6897,  -6576,  -6206,
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   -3802,  -3332,  -2902,  -2513,
   -2161,  -1835,  -1524,  -1216,
    -900,   -568,   -212,    171,
     576,    994,   1414,   1820,
    2198,   2543,   2850,   3123,
    3368,   3590,   3798,   3999,
    4197,   4397,   4600,   4805,
    5009,   5208,   5394,   5564,
    5713,   5842,   5952,   6045,
    6124,   6194,   6256,   6314,
    6368,   6420,   6470,   6517,
    6561,   6600,   6634,   6662,
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    6758,   6762,   6765,   6768,
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    6775,   6776,   6776,   6776,
    6776,   6777,   6777,   6777,
    6777,   6777,   6777,   6777,
    6777,   6777,   6777,   6777,
    6777,   6777,   6777,   6777,
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    6777,   6777,   6777,   6777,
    6777,   6777,   6777,   6776,
    6776,   6776,   6776,   6775,
    6775,   6774,   6772,   6771,
    6768,   6765,   6762,   6758,
    6754,   6749,   6743,   6736,
    6728,   6717,   6703,   6685,
    6662,   6634,   6600,   6561,
    6517,   6470,   6420,   6368,
    6314,   6256,   6194,   6124,
    6045,   5952,   5842,   5713,
    5564,   5394,   5208,   5009,
    4805,   4600,   4397,   4197,
    3999,   3798,   3590,   3368,
    3123,   2850,   2543,   2198,
    1820,   1414,    994,    576,
     171,   -212,   -568,   -900,
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   -2513,  -2902,  -3332,  -3802,
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   -6206,  -6576,  -6897,  -7179,
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   -8470,  -8798,  -9170,  -9580,
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  -11400, -11596, -11744, -11860,
  -11958, -12051, -12153, -12278,
  -12448, -12687, -13016, -13433,
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  -14767, -14774, -14775, -14775,
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   -9682,  -9682,  -9682,  -9682,
   -9679,  -9641,  -9484,  -9155,
   -8745,  -8405,  -8193,  -8082,
   -8025,  -7995,  -7975,  -7958,
   -7939,  -7913,  -7870,  -7795,
   -7665,  -7459,  -7170,  -6821,
   -6459,  -6131,  -5861,  -5651,
   -5488,  -5356,  -5240,  -5125,
   -4997,  -4842,  -4641,  -4374,
   -4026,  -3596,  -3105,  -2593,
   -2105,  -1673,  -1312,  -1018,
    -775,   -567,   -378,   -193,
       1,    217,    465,    750,
    1071,   1413,   1757,   2078,
    2359,   2590,   2775,   2921,
    3037,   3134,   3218,   3297,
    3374,   3452,   3532,   3614,
    3696,   3773,   3841,   3897,
    3941,   3973,   3996,   4013,
    4026,   4035,   4043,   4049,
    4055,   4060,   4065,   4070,
    4073,   4076,   4078,   4080,
    4081,   4082,   4082,   4082,
    4082,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4083,
    4083,   4083,   4083,   4082,
    4082,   4082,   4082,   4081,
    4080,   4078,   4076,   4073,
    4070,   4065,   4060,   4055,
    4049,   4043,   4035,   4026,
    4013,   3996,   3973,   3941,
    3897,   3841,   3773,   3696,
    3614,   3532,   3452,   3374,
    3297,   3218,   3134,   3037,
    2921,   2775,   2590,   2359,
    2078,   1757,   1413,   1071,
     750,    465,    217,      1,
    -193,   -378,   -567,   -775,
   -1018,  -1312,  -1673,  -2105,
   -2593,  -3105,  -3596,  -4026,
   -4374,  -4641,  -4842,  -4997,
   -5125,  -5240,  -5356,  -5488,
   -5651,  -5861,  -6131,  -6459,
   -6821,  -7170,  -7459,  -7665,
   -7795,  -7870,  -7913,  -7939,
   -7958,  -7975,  -7995,  -8025,
   -8082,  -8193,  -8405,  -8745,
   -9155,  -9484,  -9641,  -9679,
   -9682,  -9682,  -9682,  -9682,
   -5442,  -5442,  -5442,  -5442,
   -5442,  -5442,  -5442,  -5442,
   -5442,  -5440,  -5392,  -5180,
   -4852,  -4626,  -4538,  -4514,
   -4508,  -4506,  -4505,  -4505,
   -4504,  -4503,  -4499,  -4488,
   -4455,  -4372,  -4209,  -3971,
   -3716,  -3505,  -3363,  -3277,
   -3225,  -3191,  -3165,  -3139,
   -3107,  -3060,  -2981,  -2841,
   -2605,  -2244,  -1774,  -1262,
    -796,   -433,   -178,     -8,
     107,    191,    261,    328,
     401,    492,    612,    771,
     972,   1201,   1432,   1634,
    1787,   1892,   1959,   2000,
    2027,   2045,   2059,   2071,
    2082,   2094,   2107,   2120,
    2133,   2145,   2154,   2160,
    2164,   2166,   2167,   2167,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2168,   2168,   2168,   2168,
    2167,   2167,   2166,   2164,
    2160,   2154,   2145,   2133,
    2120,   2107,   2094,   2082,
    2071,   2059,   2045,   2027,
    2000,   1959,   1892,   1787,
    1634,   1432,   1201,    972,
     771,    612,    492,    401,
     328,    261,    191,    107,
      -8,   -178,   -433,   -796,
   -1262,  -1774,  -2244,  -2605,
   -2841,  -2981,  -3060,  -3107,
   -3139,  -3165,  -3191,  -3225,
   -3277,  -3363,  -3505,  -3716,
   -3971,  -4209,  -4372,  -4455,
   -4488,  -4499,  -4503,  -4504,
   -4505,  -4505,  -4506,  -4508,
   -4514,  -4538,  -4626,  -4852,
   -5180,  -5392,  -5440,  -5442,
   -5442,  -5442,  -5442,  -5442,
   -2672,  -2672,  -2672,  -2672,
   -2672,  -2672,  -2672,  -2672,
   -2672,  -2672,  -2667,  -2580,
   -2370,  -2270,  -2255,  -2254,
   -2254,  -2254,  -2254,  -2254,
   -2254,  -2254,  -2254,  -2254,
   -2251,  -2238,  -2186,  -2076,
   -1948,  -1862,  -1822,  -1808,
   -1802,  -1800,  -1799,  -1797,
   -1796,  -1791,  -1779,  -1741,
   -1632,  -1378,   -946,   -434,
     -10,    248,    375,    431,
     457,    471,    480,    489,
     500,    516,    544,    593,
     672,    775,    879,    958,
    1004,   1026,   1034,   1038,
    1039,   1040,   1040,   1040,
    1041,   1041,   1041,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1042,   1042,   1042,
    1042,   1041,   1041,   1041,
    1040,   1040,   1040,   1039,
    1038,   1034,   1026,   1004,
     958,    879,    775,    672,
     593,    544,    516,    500,
     489,    480,    471,    457,
     431,    375,    248,    -10,
    -434,   -946,  -1378,  -1632,
   -1741,  -1779,  -1791,  -1796,
   -1797,  -1799,  -1800,  -1802,
   -1808,  -1822,  -1862,  -1948,
   -2076,  -2186,  -2238,  -2251,
   -2254,  -2254,  -2254,  -2254,
   -2254,  -2254,  -2254,  -2254,
   -2254,  -2255,  -2270,  -2370,
   -2580,  -2667,  -2672,  -2672,
   -2672,  -2672,  -2672,  -2672,
   -1301,  -1301,  -1301,  -1301,
   -1301,  -1301,  -1301,  -1301,
   -1301,  -1301,  -1301,  -1286,
   -1200,  -1180,  -1180,  -1180,
   -1180,  -1180,  -1180,  -1180,
   -1180,  -1180,  -1180,  -1180,
   -1180,  -1179,  -1174,  -1150,
   -1119,  -1104,  -1101,  -1101,
   -1100,  -1100,  -1100,  -1100,
   -1100,  -1100,  -1100,  -1097,
   -1074,   -948,   -584,    -72,
     280,    410,    441,    447,
     448,    449,    449,    449,
     449,    450,    451,    456,
     468,    489,    510,    522,
     526,    527,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    528,    528,
     528,    528,    527,    526,
     522,    510,    489,    468,
     456,    451,    450,    449,
     449,    449,    449,    448,
     447,    441,    410,    280,
     -72,   -584,   -948,  -1074,
   -1097,  -1100,  -1100,  -1100,
   -1100,  -1100,  -1100,  -1100,
   -1101,  -1101,  -1104,  -1119,
   -1150,  -1174,  -1179,  -1180,
   -1180,  -1180,  -1180,  -1180,
   -1180,  -1180,  -1180,  -1180,
   -1180,  -1180,  -1180,  -1200,
   -1286,  -1301,  -1301,  -1301,
   -1301,  -1301,  -1301,  -1301,
  -12451, -12598, -12712, -12778,
  -12778, -12712, -12598, -12451,
  -12272, -12055, -11803, -11517,
  -11194, -10833, -10441, -10025,
   -9587,  -9130,  -8656,  -8170,
   -7674,  -7168,  -6659,  -6150,
   -5640,  -5128,  -4619,  -4117,
   -3625,  -3144,  -2679,  -2234,
   -1807,  -1394,   -998,   -620,
    -262,     75,    390,    682,
     954,   1205,   1435,   1640,
    1823,   1987,   2132,   2260,
    2373,   2470,   2549,   2608,
    2650,   2679,   2698,   2710,
    2716,   2716,   2708,   2690,
    2663,   2630,   2592,   2553,
    2513,   2472,   2428,   2379,
    2327,   2274,   2220,   2166,
    2115,   2065,   2015,   1965,
    1919,   1876,   1837,   1799,
    1762,   1730,   1702,   1679,
    1664,   1657,   1658,   1664,
    1674,   1689,   1711,   1743,
    1785,   1834,   1887,   1943,
    2004,   2070,   2141,   2218,
    2300,   2385,   2470,   2555,
    2642,   2732,   2824,   2917,
    3011,   3101,   3186,   3269,
    3352,   3437,   3521,   3604,
    3685,   3761,   3831,   3897,
    3960,   4022,   4079,   4132,
    4181,   4224,   4258,   4285,
    4310,   4332,   4346,   4352,
    4352,   4346,   4332,   4310,
    4285,   4258,   4224,   4181,
    4132,   4079,   4022,   3960,
    3897,   3831,   3761,   3685,
    3604,   3521,   3437,   3352,
    3269,   3186,   3101,   3011,
    2917,   2824,   2732,   2642,
    2555,   2470,   2385,   2300,
    2218,   2141,   2070,   2004,
    1943,   1887,   1834,   1785,
    1743,   1711,   1689,   1674,
    1664,   1658,   1657,   1664,
    1679,   1702,   1730,   1762,
    1799,   1837,   1876,   1919,
    1965,   2015,   2065,   2115,
    2166,   2220,   2274,   2327,
    2379,   2428,   2472,   2513,
    2553,   2592,   2630,   2663,
    2690,   2708,   2716,   2716,
    2710,   2698,   2679,   2650,
    2608,   2549,   2470,   2373,
    2260,   2132,   1987,   1823,
    1640,   1435,   1205,    954,
     682,    390,     75,   -262,
    -620,   -998,  -1394,  -1807,
   -2234,  -2679,  -3144,  -3625,
   -4117,  -4619,  -5128,  -5640,
   -6150,  -6659,  -7168,  -7674,
   -8170,  -8656,  -9130,  -9587,
  -10025, -10441, -10833, -11194,
  -11517, -11803, -12055, -12272,
  -12451, -12598, -12712, -12778,
  -12242, -12392, -12512, -12584,
  -12584, -12512, -12392, -12242,
  -12064, -11850, -11595, -11298,
  -10957, -10578, -10173,  -9753,
   -9322,  -8874,  -8405,  -7915,
   -7410,  -6898,  -6389,  -5887,
   -5389,  -4890,  -4390,  -3890,
   -3397,  -2917,  -2454,  -2008,
   -1573,  -1144,   -722,   -312,
      82,    460,    822,   1167,
    1500,   1821,   2130,   2426,
    2706,   2969,   3216,   3451,
    3675,   3888,   4088,   4272,
    4440,   4596,   4742,   4876,
    4998,   5106,   5200,   5278,
    5342,   5392,   5430,   5454,
    5464,   5455,   5428,   5387,
    5337,   5276,   5198,   5103,
    4991,   4870,   4741,   4603,
    4456,   4301,   4141,   3975,
    3805,   3636,   3468,   3303,
    3140,   2979,   2820,   2667,
    2520,   2382,   2251,   2129,
    2012,   1898,   1787,   1683,
    1589,   1503,   1421,   1340,
    1259,   1180,   1103,   1028,
     957,    887,    817,    745,
     672,    596,    522,    450,
     379,    307,    230,    152,
      74,      1,    -68,   -132,
    -193,   -255,   -319,   -381,
    -435,   -481,   -519,   -552,
    -577,   -599,   -617,   -629,
    -629,   -617,   -599,   -577,
    -552,   -519,   -481,   -435,
    -381,   -319,   -255,   -193,
    -132,    -68,      1,     74,
     152,    230,    307,    379,
     450,    522,    596,    672,
     745,    817,    887,    957,
    1028,   1103,   1180,   1259,
    1340,   1421,   1503,   1589,
    1683,   1787,   1898,   2012,
    2129,   2251,   2382,   2520,
    2667,   2820,   2979,   3140,
    3303,   3468,   3636,   3805,
    3975,   4141,   4301,   4456,
    4603,   4741,   4870,   4991,
    5103,   5198,   5276,   5337,
    5387,   5428,   5455,   5464,
    5454,   5430,   5392,   5342,
    5278,   5200,   5106,   4998,
    4876,   4742,   4596,   4440,
    4272,   4088,   3888,   3675,
    3451,   3216,   2969,   2706,
    2426,   2130,   1821,   1500,
    1167,    822,    460,     82,
    -312,   -722,  -1144,  -1573,
   -2008,  -2454,  -2917,  -3397,
   -3890,  -4390,  -4890,  -5389,
   -5887,  -6389,  -6898,  -7410,
   -7915,  -8405,  -8874,  -9322,
   -9753, -10173, -10578, -10957,
  -11298, -11595, -11850, -12064,
  -12242, -12392, -12512, -12584,
   -8702,  -8890,  -9039,  -9126,
   -9126,  -9039,  -8890,  -8702,
   -8478,  -8212,  -7901,  -7545,
   -7142,  -6697,  -6222,  -5733,
   -5234,  -4727,  -4217,  -3705,
   -3194,  -2689,  -2197,  -1726,
   -1274,   -844,   -437,    -54,
     303,    633,    932,   1202,
    1446,   1667,   1864,   2034,
    2178,   2295,   2386,   2455,
    2507,   2545,   2565,   2566,
    2551,   2522,   2478,   2422,
    2356,   2281,   2193,   2093,
    1987,   1878,   1765,   1648,
    1527,   1403,   1273,   1138,
    1005,    880,    763,    654,
     551,    455,    362,    277,
     204,    145,    104,     81,
      76,     87,    108,    139,
     187,    254,    339,    438,
     552,    678,    815,    958,
    1108,   1263,   1423,   1586,
    1749,   1909,   2063,   2208,
    2344,   2468,   2573,   2661,
    2732,   2786,   2821,   2836,
    2830,   2800,   2743,   2662,
    2561,   2445,   2311,   2161,
    1997,   1820,   1628,   1427,
    1222,   1016,    806,    595,
     385,    179,    -23,   -218,
    -401,   -569,   -727,   -875,
   -1012,  -1133,  -1238,  -1324,
   -1393,  -1445,  -1481,  -1501,
   -1501,  -1481,  -1445,  -1393,
   -1324,  -1238,  -1133,  -1012,
    -875,   -727,   -569,   -401,
    -218,    -23,    179,    385,
     595,    806,   1016,   1222,
    1427,   1628,   1820,   1997,
    2161,   2311,   2445,   2561,
    2662,   2743,   2800,   2830,
    2836,   2821,   2786,   2732,
    2661,   2573,   2468,   2344,
    2208,   2063,   1909,   1749,
    1586,   1423,   1263,   1108,
     958,    815,    678,    552,
     438,    339,    254,    187,
     139,    108,     87,     76,
      81,    104,    145,    204,
     277,    362,    455,    551,
     654,    763,    880,   1005,
    1138,   1273,   1403,   1527,
    1648,   1765,   1878,   1987,
    2093,   2193,   2281,   2356,
    2422,   2478,   2522,   2551,
    2566,   2565,   2545,   2507,
    2455,   2386,   2295,   2178,
    2034,   1864,   1667,   1446,
    1202,    932,    633,    303,
     -54,   -437,   -844,  -1274,
   -1726,  -2197,  -2689,  -3194,
   -3705,  -4217,  -4727,  -5234,
   -5733,  -6222,  -6697,  -7142,
   -7545,  -7901,  -8212,  -8478,
   -8702,  -8890,  -9039,  -9126,
  -13319, -13432, -13564, -13663,
  -13663, -13564, -13432, -13319,
  -13219, -13092, -12914, -12691,
  -12430, -12139, -11831, -11517,
  -11192, -10841, -10458, -10048,
   -9618,  -9174,  -8721,  -8266,
   -7805,  -7331,  -6837,  -6331,
   -5824,  -5322,  -4823,  -4321,
   -3812,  -3300,  -2795,  -2306,
   -1829,  -1358,   -890,   -433,
       9,    435,    845,   1235,
    1604,   1958,   2303,   2638,
    2954,   3246,   3512,   3753,
    3972,   4178,   4380,   4575,
    4744,   4869,   4954,   5024,
    5099,   5178,   5245,   5285,
    5297,   5281,   5244,   5199,
    5159,   5124,   5079,   5010,
    4916,   4810,   4703,   4600,
    4498,   4394,   4280,   4154,
    4019,   3883,   3755,   3637,
    3524,   3408,   3287,   3167,
    3053,   2948,   2848,   2755,
    2671,   2600,   2536,   2472,
    2409,   2353,   2310,   2278,
    2251,   2223,   2197,   2177,
    2169,   2169,   2173,   2179,
    2187,   2198,   2217,   2244,
    2278,   2311,   2337,   2361,
    2390,   2427,   2470,   2516,
    2561,   2599,   2625,   2639,
    2652,   2678,   2715,   2753,
    2778,   2783,   2774,   2763,
    2763,   2774,   2783,   2778,
    2753,   2715,   2678,   2652,
    2639,   2625,   2599,   2561,
    2516,   2470,   2427,   2390,
    2361,   2337,   2311,   2278,
    2244,   2217,   2198,   2187,
    2179,   2173,   2169,   2169,
    2177,   2197,   2223,   2251,
    2278,   2310,   2353,   2409,
    2472,   2536,   2600,   2671,
    2755,   2848,   2948,   3053,
    3167,   3287,   3408,   3524,
    3637,   3755,   3883,   4019,
    4154,   4280,   4394,   4498,
    4600,   4703,   4810,   4916,
    5010,   5079,   5124,   5159,
    5199,   5244,   5281,   5297,
    5285,   5245,   5178,   5099,
    5024,   4954,   4869,   4744,
    4575,   4380,   4178,   3972,
    3753,   3512,   3246,   2954,
    2638,   2303,   1958,   1604,
    1235,    845,    435,      9,
    -433,   -890,  -1358,  -1829,
   -2306,  -2795,  -3300,  -3812,
   -4321,  -4823,  -5322,  -5824,
   -6331,  -6837,  -7331,  -7805,
   -8266,  -8721,  -9174,  -9618,
  -10048, -10458, -10841, -11192,
  -11517, -11831, -12139, -12430,
  -12691, -12914, -13092, -13219,
  -13319, -13432, -13564, -13663,
   -8380,  -8806,  -9224,  -9492,
   -9492,  -9224,  -8806,  -8380,
   -8011,  -7680,  -7337,  -6941,
   -6479,  -5969,  -5457,  -5002,
   -4642,  -4373,  -4158,  -3958,
   -3761,  -3582,  -3439,  -3337,
   -3274,  -3250,  -3270,  -3333,
   -3419,  -3510,  -3591,  -3653,
   -3685,  -3679,  -3641,  -3587,
   -3527,  -3458,  -3365,  -3223,
   -3010,  -2723,  -2382,  -2027,
   -1688,  -1375,  -1078,   -778,
    -462,   -132,    192,    481,
     718,    903,   1053,   1188,
    1320,   1445,   1548,   1615,
    1649,   1654,   1638,   1607,
    1568,   1530,   1503,   1495,
    1510,   1542,   1583,   1624,
    1670,   1730,   1814,   1920,
    2040,   2159,   2271,   2376,
    2480,   2586,   2694,   2804,
    2921,   3045,   3169,   3281,
    3371,   3437,   3477,   3500,
    3516,   3533,   3554,   3572,
    3572,   3538,   3464,   3355,
    3227,   3097,   2975,   2861,
    2752,   2633,   2491,   2323,
    2149,   2005,   1919,   1892,
    1901,   1918,   1925,   1925,
    1937,   1980,   2066,   2189,
    2333,   2479,   2614,   2729,
    2826,   2909,   2984,   3057,
    3129,   3194,   3245,   3274,
    3274,   3245,   3194,   3129,
    3057,   2984,   2909,   2826,
    2729,   2614,   2479,   2333,
    2189,   2066,   1980,   1937,
    1925,   1925,   1918,   1901,
    1892,   1919,   2005,   2149,
    2323,   2491,   2633,   2752,
    2861,   2975,   3097,   3227,
    3355,   3464,   3538,   3572,
    3572,   3554,   3533,   3516,
    3500,   3477,   3437,   3371,
    3281,   3169,   3045,   2921,
    2804,   2694,   2586,   2480,
    2376,   2271,   2159,   2040,
    1920,   1814,   1730,   1670,
    1624,   1583,   1542,   1510,
    1495,   1503,   1530,   1568,
    1607,   1638,   1654,   1649,
    1615,   1548,   1445,   1320,
    1188,   1053,    903,    718,
     481,    192,   -132,   -462,
    -778,  -1078,  -1375,  -1688,
   -2027,  -2382,  -2723,  -3010,
   -3223,  -3365,  -3458,  -3527,
   -3587,  -3641,  -3679,  -3685,
   -3653,  -3591,  -3510,  -3419,
   -3333,  -3270,  -3250,  -3274,
   -3337,  -3439,  -3582,  -3761,
   -3958,  -4158,  -4373,  -4642,
   -5002,  -5457,  -5969,  -6479,
   -6941,  -7337,  -7680,  -8011,
   -8380,  -8806,  -9224,  -9492,
   -8814,  -9273,  -9685,  -9934,
   -9934,  -9685,  -9273,  -8814,
   -8401,  -8075,  -7831,  -7627,
   -7417,  -7170,  -6886,  -6581,
   -6262,  -5918,  -5531,  -5088,
   -4597,  -4085,  -3593,  -3157,
   -2794,  -2499,  -2247,  -2013,
   -1779,  -1545,  -1319,  -1108,
    -916,   -733,   -549,   -355,
    -152,     57,    260,    442,
     588,    689,    737,    741,
     718,    700,    711,    770,
     876,   1017,   1170,   1314,
    1435,   1528,   1594,   1634,
    1654,   1661,   1663,   1668,
    1692,   1751,   1848,   1970,
    2097,   2208,   2294,   2354,
    2403,   2458,   2531,   2619,
    2708,   2780,   2829,   2859,
    2882,   2912,   2960,   3029,
    3114,   3199,   3266,   3298,
    3290,   3249,   3190,   3124,
    3059,   2992,   2916,   2831,
    2742,   2654,   2573,   2496,
    2413,   2309,   2173,   2004,
    1816,   1632,   1468,   1333,
    1219,   1115,   1005,    882,
     750,    626,    531,    474,
     449,    440,    432,    416,
     395,    382,    391,    425,
     478,    538,    591,    629,
     653,    669,    686,    709,
     737,    766,    789,    803,
     803,    789,    766,    737,
     709,    686,    669,    653,
     629,    591,    538,    478,
     425,    391,    382,    395,
     416,    432,    440,    449,
     474,    531,    626,    750,
     882,   1005,   1115,   1219,
    1333,   1468,   1632,   1816,
    2004,   2173,   2309,   2413,
    2496,   2573,   2654,   2742,
    2831,   2916,   2992,   3059,
    3124,   3190,   3249,   3290,
    3298,   3266,   3199,   3114,
    3029,   2960,   2912,   2882,
    2859,   2829,   2780,   2708,
    2619,   2531,   2458,   2403,
    2354,   2294,   2208,   2097,
    1970,   1848,   1751,   1692,
    1668,   1663,   1661,   1654,
    1634,   1594,   1528,   1435,
    1314,   1170,   1017,    876,
     770,    711,    700,    718,
     741,    737,    689,    588,
     442,    260,     57,   -152,
    -355,   -549,   -733,   -916,
   -1108,  -1319,  -1545,  -1779,
   -2013,  -2247,  -2499,  -2794,
   -3157,  -3593,  -4085,  -4597,
   -5088,  -5531,  -5918,  -6262,
   -6581,  -6886,  -7170,  -7417,
   -7627,  -7831,  -8075,  -8401,
   -8814,  -9273,  -9685,  -9934,
  -12502, -12761, -13043, -13233,
  -13233, -13043, -12761, -12502,
  -12325, -12236, -12203, -12161,
  -12042, -11815, -11515, -11190,
  -10862, -10531, -10199,  -9863,
   -9505,  -9111,  -8694,  -8281,
   -7883,  -7497,  -7115,  -6732,
   -6331,  -5891,  -5409,  -4903,
   -4391,  -3890,  -3424,  -3016,
   -2661,  -2323,  -1959,  -1545,
   -1081,   -587,   -104,    329,
     700,   1032,   1359,   1696,
    2042,   2387,   2720,   3033,
    3333,   3635,   3946,   4259,
    4557,   4829,   5070,   5276,
    5450,   5612,   5782,   5966,
    6156,   6341,   6513,   6662,
    6783,   6878,   6954,   7011,
    7044,   7054,   7057,   7067,
    7083,   7094,   7090,   7066,
    7020,   6951,   6862,   6751,
    6615,   6456,   6288,   6131,
    5996,   5876,   5749,   5594,
    5398,   5160,   4898,   4634,
    4386,   4156,   3937,   3720,
    3494,   3256,   3007,   2756,
    2509,   2262,   2008,   1741,
    1465,   1196,    948,    732,
     541,    355,    159,    -52,
    -267,   -474,   -663,   -839,
   -1007,  -1169,  -1316,  -1434,
   -1515,  -1567,  -1611,  -1667,
   -1745,  -1837,  -1922,  -1973,
   -1973,  -1922,  -1837,  -1745,
   -1667,  -1611,  -1567,  -1515,
   -1434,  -1316,  -1169,  -1007,
    -839,   -663,   -474,   -267,
     -52,    159,    355,    541,
     732,    948,   1196,   1465,
    1741,   2008,   2262,   2509,
    2756,   3007,   3256,   3494,
    3720,   3937,   4156,   4386,
    4634,   4898,   5160,   5398,
    5594,   5749,   5876,   5996,
    6131,   6288,   6456,   6615,
    6751,   6862,   6951,   7020,
    7066,   7090,   7094,   7083,
    7067,   7057,   7054,   7044,
    7011,   6954,   6878,   6783,
    6662,   6513,   6341,   6156,
    5966,   5782,   5612,   5450,
    5276,   5070,   4829,   4557,
    4259,   3946,   3635,   3333,
    3033,   2720,   2387,   2042,
    1696,   1359,   1032,    700,
     329,   -104,   -587,  -1081,
   -1545,  -1959,  -2323,  -2661,
   -3016,  -3424,  -3890,  -4391,
   -4903,  -5409,  -5891,  -6331,
   -6732,  -7115,  -7497,  -7883,
   -8281,  -8694,  -9111,  -9505,
   -9863, -10199, -10531, -10862,
  -11190, -11515, -11815, -12042,
  -12161, -12203, -12236, -12325,
  -12502, -12761, -13043, -13233,
  -11873, -12028, -12237, -12396,
  -12396, -12237, -12028, -11873,
  -11783, -11707, -11592, -11405,
  -11137, -10814, -10489, -10193,
   -9903,  -9577,  -9201,  -8791,
   -8363,  -7924,  -7484,  -7048,
   -6609,  -6152,  -5675,  -5188,
   -4699,  -4209,  -3711,  -3204,
   -2692,  -2186,  -1699,  -1230,
    -772,   -313,    155,    638,
    1122,   1580,   1990,   2364,
    2737,   3131,   3538,   3932,
    4290,   4601,   4878,   5152,
    5447,   5752,   6032,   6266,
    6463,   6643,   6820,   6999,
    7181,   7351,   7483,   7570,
    7636,   7705,   7784,   7855,
    7899,   7907,   7881,   7836,
    7794,   7762,   7723,   7654,
    7546,   7405,   7249,   7095,
    6948,   6794,   6617,   6413,
    6194,   5971,   5743,   5508,
    5261,   4995,   4707,   4406,
    4108,   3819,   3526,   3217,
    2896,   2574,   2254,   1931,
    1606,   1278,    943,    604,
     266,    -62,   -377,   -678,
    -967,  -1256,  -1555,  -1864,
   -2162,  -2435,  -2682,  -2918,
   -3153,  -3392,  -3628,  -3844,
   -4025,  -4172,  -4307,  -4448,
   -4594,  -4730,  -4840,  -4923,
   -4982,  -5024,  -5052,  -5067,
   -5067,  -5052,  -5024,  -4982,
   -4923,  -4840,  -4730,  -4594,
   -4448,  -4307,  -4172,  -4025,
   -3844,  -3628,  -3392,  -3153,
   -2918,  -2682,  -2435,  -2162,
   -1864,  -1555,  -1256,   -967,
    -678,   -377,    -62,    266,
     604,    943,   1278,   1606,
    1931,   2254,   2574,   2896,
    3217,   3526,   3819,   4108,
    4406,   4707,   4995,   5261,
    5508,   5743,   5971,   6194,
    6413,   6617,   6794,   6948,
    7095,   7249,   7405,   7546,
    7654,   7723,   7762,   7794,
    7836,   7881,   7907,   7899,
    7855,   7784,   7705,   7636,
    7570,   7483,   7351,   7181,
    6999,   6820,   6643,   6463,
    6266,   6032,   5752,   5447,
    5152,   4878,   4601,   4290,
    3932,   3538,   3131,   2737,
    2364,   1990,   1580,   1122,
     638,    155,   -313,   -772,
   -1230,  -1699,  -2186,  -2692,
   -3204,  -3711,  -4209,  -4699,
   -5188,  -5675,  -6152,  -6609,
   -7048,  -7484,  -7924,  -8363,
   -8791,  -9201,  -9577,  -9903,
  -10193, -10489, -10814, -11137,
  -11405, -11592, -11707, -11783,
  -11873, -12028, -12237, -12396,
   -3082,  -3584,  -4096,  -4440,
   -4440,  -4096,  -3584,  -3082,
   -2643,  -2240,  -1863,  -1518,
   -1184,   -825,   -438,    -50,
     331,    714,   1096,   1446,
    1734,   1943,   2063,   2092,
    2040,   1930,   1786,   1626,
    1464,   1307,   1138,    940,
     723,    516,    340,    195,
      84,     22,     16,     51,
     103,    157,    203,    229,
     233,    230,    232,    236,
     225,    201,    179,    170,
     158,    120,     43,    -65,
    -183,   -297,   -392,   -455,
    -486,   -504,   -534,   -592,
    -672,   -758,   -834,   -881,
    -877,   -813,   -707,   -590,
    -478,   -372,   -273,   -196,
    -144,   -104,    -53,     14,
      91,    167,    236,    301,
     367,    438,    514,    590,
     657,    709,    740,    754,
     766,    789,    820,    836,
     826,    807,    804,    819,
     828,    809,    764,    710,
     663,    628,    605,    590,
     574,    546,    491,    401,
     280,    151,     37,    -50,
    -117,   -177,   -246,   -335,
    -442,   -554,   -650,   -722,
    -776,   -824,   -877,   -942,
   -1019,  -1101,  -1172,  -1213,
   -1213,  -1172,  -1101,  -1019,
    -942,   -877,   -824,   -776,
    -722,   -650,   -554,   -442,
    -335,   -246,   -177,   -117,
     -50,     37,    151,    280,
     401,    491,    546,    574,
     590,    605,    628,    663,
     710,    764,    809,    828,
     819,    804,    807,    826,
     836,    820,    789,    766,
     754,    740,    709,    657,
     590,    514,    438,    367,
     301,    236,    167,     91,
      14,    -53,   -104,   -144,
    -196,   -273,   -372,   -478,
    -590,   -707,   -813,   -877,
    -881,   -834,   -758,   -672,
    -592,   -534,   -504,   -486,
    -455,   -392,   -297,   -183,
     -65,     43,    120,    158,
     170,    179,    201,    225,
     236,    232,    230,    233,
     229,    203,    157,    103,
      51,     16,     22,     84,
     195,    340,    516,    723,
     940,   1138,   1307,   1464,
    1626,   1786,   1930,   2040,
    2092,   2063,   1943,   1734,
    1446,   1096,    714,    331,
     -50,   -438,   -825,  -1184,
   -1518,  -1863,  -2240,  -2643,
   -3082,  -3584,  -4096,  -4440,
   -3159,  -3609,  -4121,  -4487,
   -4487,  -4121,  -3609,  -3159,
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   -1000,  -1295,  -1621,  -1990,
   -2392,  -2791,  -3138,  -3417,
   -3682,  -4028,  -4493,  -4996,
   -5413,  -5704,  -5956,  -6285,
   -6718,  -7179,  -7582,  -7897,
   -8140,  -8340,  -8539,  -8804,
   -9165,  -9533,  -9737,  -9728,
   -9705,  -9944, -10456, -10898,
   -4318,  -4425,  -4937,  -5440,
   -5440,  -4937,  -4425,  -4318,
   -4530,  -4677,  -4549,  -4257,
   -4004,  -3863,  -3790,  -3731,
   -3649,  -3513,  -3314,  -3081,
   -2863,  -2699,  -2596,  -2524,
   -2423,  -2248,  -2027,  -1846,
   -1758,  -1715,  -1625,  -1454,
   -1254,  -1099,  -1015,   -971,
    -905,   -778,   -594,   -412,
    -289,   -231,   -181,    -72,
     107,    305,    454,    530,
     572,    649,    795,    979,
    1126,   1195,   1214,   1245,
    1326,   1447,   1578,   1689,
    1757,   1775,   1769,   1787,
    1859,   1964,   2054,   2099,
    2100,   2068,   2019,   1990,
    2013,   2071,   2090,   2020,
    1901,   1827,   1843,   1899,
    1908,   1834,   1706,   1587,
    1523,   1523,   1549,   1541,
    1467,   1365,   1303,   1307,
    1327,   1301,   1236,   1192,
    1188,   1174,   1105,   1030,
    1037,   1128,   1192,   1134,
     994,    893,    883,    906,
     887,    822,    751,    703,
     672,    649,    618,    564,
     491,    428,    400,    380,
     326,    242,    180,    167,
     174,    156,    115,     92,
     101,    112,     99,     78,
      78,     99,    112,    101,
      92,    115,    156,    174,
     167,    180,    242,    326,
     380,    400,    428,    491,
     564,    618,    649,    672,
     703,    751,    822,    887,
     906,    883,    893,    994,
    1134,   1192,   1128,   1037,
    1030,   1105,   1174,   1188,
    1192,   1236,   1301,   1327,
    1307,   1303,   1365,   1467,
    1541,   1549,   1523,   1523,
    1587,   1706,   1834,   1908,
    1899,   1843,   1827,   1901,
    2020,   2090,   2071,   2013,
    1990,   2019,   2068,   2100,
    2099,   2054,   1964,   1859,
    1787,   1769,   1775,   1757,
    1689,   1578,   1447,   1326,
    1245,   1214,   1195,   1126,
     979,    795,    649,    572,
     530,    454,    305,    107,
     -72,   -181,   -231,   -289,
    -412,   -594,   -778,   -905,
    -971,  -1015,  -1099,  -1254,
   -1454,  -1625,  -1715,  -1758,
   -1846,  -2027,  -2248,  -2423,
   -2524,  -2596,  -2699,  -2863,
   -3081,  -3314,  -3513,  -3649,
   -3731,  -3790,  -3863,  -4004,
   -4257,  -4549,  -4677,  -4530,
   -4318,  -4425,  -4937,  -5440,
  -20214, -20305, -20379, -20423,
  -20423, -20379, -20305, -20214,
  -20111, -19995, -19872, -19746,
  -19618, -19485, -19346, -19205,
  -19062, -18913, -18760, -18604,
  -18442, -18267, -18078, -17874,
  -17653, -17413, -17151, -16870,
  -16571, -16256, -15927, -15589,
  -15241, -14889, -14535, -14184,
  -13837, -13491, -13145, -12798,
  -12445, -12086, -11719, -11340,
  -10948, -10542, -10121,  -9688,
   -9242,  -8783,  -8315,  -7839,
   -7360,  -6877,  -6390,  -5903,
   -5418,  -4938,  -4464,  -3998,
   -3538,  -3081,  -2622,  -2158,
   -1687,  -1209,   -723,   -230,
     271,    776,   1284,   1794,
    2306,   2818,   3328,   3834,
    4332,   4823,   5303,   5771,
    6227,   6669,   7099,   7519,
    7934,   8347,   8760,   9174,
    9591,  10012,  10437,  10863,
   11290,  11715,  12136,  12551,
   12956,  13349,  13728,  14091,
   14438,  14768,  15080,  15376,
   15657,  15927,  16189,  16441,
   16686,  16925,  17160,  17390,
   17618,  17844,  18069,  18290,
   18504,  18707,  18897,  19070,
   19224,  19357,  19471,  19567,
   19644,  19705,  19751,  19784,
   19807,  19820,  19826,  19828,
   19828,  19826,  19820,  19807,
   19784,  19751,  19705,  19644,
   19567,  19471,  19357,  19224,
   19070,  18897,  18707,  18504,
   18290,  18069,  17844,  17618,
   17390,  17160,  16925,  16686,
   16441,  16189,  15927,  15657,
   15376,  15080,  14768,  14438,
   14091,  13728,  13349,  12956,
   12551,  12136,  11715,  11290,
   10863,  10437,  10012,   9591,
    9174,   8760,   8347,   7934,
    7519,   7099,   6669,   6227,
    5771,   5303,   4823,   4332,
    3834,   3328,   2818,   2306,
    1794,   1284,    776,    271,
    -230,   -723,  -1209,  -1687,
   -2158,  -2622,  -3081,  -3538,
   -3998,  -4464,  -4938,  -5418,
   -5903,  -6390,  -6877,  -7360,
   -7839,  -8315,  -8783,  -9242,
   -9688, -10121, -10542, -10948,
  -11340, -11719, -12086, -12445,
  -12798, -13145, -13491, -13837,
  -14184, -14535, -14889, -15241,
  -15589, -15927, -16256, -16571,
  -16870, -17151, -17413, -17653,
  -17874, -18078, -18267, -18442,
  -18604, -18760, -18913, -19062,
  -19205, -19346, -19485, -19618,
  -19746, -19872, -19995, -20111,
  -20214, -20305, -20379, -20423,
  -11585, -11732, -11846, -11911,
  -11911, -11846, -11732, -11585,
  -11410, -11211, -10993, -10765,
  -10528, -10279, -10019,  -9749,
   -9464,  -9158,  -8827,  -8470,
   -8087,  -7674,  -7233,  -6769,
   -6286,  -5789,  -5281,  -4769,
   -4257,  -3747,  -3243,  -2748,
   -2263,  -1786,  -1314,   -845,
    -377,     95,    573,   1058,
    1544,   2027,   2504,   2971,
    3423,   3857,   4267,   4652,
    5013,   5349,   5663,   5955,
    6230,   6488,   6733,   6963,
    7179,   7383,   7572,   7745,
    7898,   8032,   8142,   8223,
    8273,   8292,   8280,   8239,
    8173,   8087,   7987,   7878,
    7761,   7640,   7512,   7374,
    7223,   7060,   6880,   6680,
    6456,   6209,   5941,   5654,
    5352,   5041,   4727,   4412,
    4098,   3786,   3480,   3180,
    2885,   2592,   2302,   2014,
    1724,   1430,   1128,    820,
     505,    186,   -133,   -450,
    -758,  -1054,  -1333,  -1596,
   -1842,  -2072,  -2288,  -2492,
   -2686,  -2870,  -3049,  -3224,
   -3399,  -3571,  -3739,  -3899,
   -4049,  -4184,  -4302,  -4402,
   -4486,  -4551,  -4599,  -4634,
   -4660,  -4678,  -4689,  -4692,
   -4692,  -4689,  -4678,  -4660,
   -4634,  -4599,  -4551,  -4486,
   -4402,  -4302,  -4184,  -4049,
   -3899,  -3739,  -3571,  -3399,
   -3224,  -3049,  -2870,  -2686,
   -2492,  -2288,  -2072,  -1842,
   -1596,  -1333,  -1054,   -758,
    -450,   -133,    186,    505,
     820,   1128,   1430,   1724,
    2014,   2302,   2592,   2885,
    3180,   3480,   3786,   4098,
    4412,   4727,   5041,   5352,
    5654,   5941,   6209,   6456,
    6680,   6880,   7060,   7223,
    7374,   7512,   7640,   7761,
    7878,   7987,   8087,   8173,
    8239,   8280,   8292,   8273,
    8223,   8142,   8032,   7898,
    7745,   7572,   7383,   7179,
    6963,   6733,   6488,   6230,
    5955,   5663,   5349,   5013,
    4652,   4267,   3857,   3423,
    2971,   2504,   2027,   1544,
    1058,    573,     95,   -377,
    -845,  -1314,  -1786,  -2263,
   -2748,  -3243,  -3747,  -4257,
   -4769,  -5281,  -5789,  -6286,
   -6769,  -7233,  -7674,  -8087,
   -8470,  -8827,  -9158,  -9464,
   -9749, -10019, -10279, -10528,
  -10765, -10993, -11211, -11410,
  -11585, -11732, -11846, -11911,
  -20089, -20198, -20283, -20331,
  -20331, -20283, -20198, -20089,
  -19957, -19802, -19627, -19439,
  -19240, -19026, -18798, -18555,
  -18297, -18020, -17721, -17400,
  -17056, -16689, -16299, -15888,
  -15461, -15021, -14571, -14113,
  -13649, -13184, -12718, -12253,
  -11787, -11320, -10851, -10378,
   -9899,  -9411,  -8914,  -8411,
   -7904,  -7393,  -6881,  -6372,
   -5871,  -5378,  -4897,  -4429,
   -3974,  -3532,  -3099,  -2675,
   -2259,  -1848,  -1439,  -1031,
    -626,   -224,    174,    564,
     945,   1315,   1673,   2018,
    2349,   2665,   2968,   3258,
    3538,   3810,   4075,   4338,
    4600,   4861,   5119,   5375,
    5628,   5877,   6121,   6355,
    6577,   6787,   6986,   7175,
    7355,   7530,   7703,   7879,
    8058,   8240,   8426,   8615,
    8806,   8997,   9189,   9379,
    9564,   9743,   9917,  10085,
   10245,  10396,  10541,  10683,
   10824,  10966,  11109,  11254,
   11402,  11551,  11703,  11854,
   12002,  12141,  12270,  12388,
   12496,  12594,  12681,  12759,
   12831,  12901,  12970,  13037,
   13101,  13163,  13222,  13277,
   13325,  13364,  13392,  13407,
   13407,  13392,  13364,  13325,
   13277,  13222,  13163,  13101,
   13037,  12970,  12901,  12831,
   12759,  12681,  12594,  12496,
   12388,  12270,  12141,  12002,
   11854,  11703,  11551,  11402,
   11254,  11109,  10966,  10824,
   10683,  10541,  10396,  10245,
   10085,   9917,   9743,   9564,
    9379,   9189,   8997,   8806,
    8615,   8426,   8240,   8058,
    7879,   7703,   7530,   7355,
    7175,   6986,   6787,   6577,
    6355,   6121,   5877,   5628,
    5375,   5119,   4861,   4600,
    4338,   4075,   3810,   3538,
    3258,   2968,   2665,   2349,
    2018,   1673,   1315,    945,
     564,    174,   -224,   -626,
   -1031,  -1439,  -1848,  -2259,
   -2675,  -3099,  -3532,  -3974,
   -4429,  -4897,  -5378,  -5871,
   -6372,  -6881,  -7393,  -7904,
   -8411,  -8914,  -9411,  -9899,
  -10378, -10851, -11320, -11787,
  -12253, -12718, -13184, -13649,
  -14113, -14571, -15021, -15461,
  -15888, -16299, -16689, -17056,
  -17400, -17721, -18020, -18297,
  -18555, -18798, -19026, -19240,
  -19439, -19627, -19802, -19957,
  -20089, -20198, -20283, -20331,
  -19619, -19879, -20067, -20168,
  -20168, -20067, -19879, -19619,
  -19295, -18916, -18494, -18041,
  -17563, -17066, -16558, -16046,
  -15536, -15032, -14541, -14068,
  -13615, -13181, -12764, -12362,
  -11975, -11598, -11228, -10864,
  -10504, -10148,  -9796,  -9447,
   -9102,  -8760,  -8420,  -8080,
   -7740,  -7397,  -7053,  -6709,
   -6364,  -6019,  -5675,  -5334,
   -4993,  -4651,  -4306,  -3957,
   -3601,  -3240,  -2875,  -2509,
   -2148,  -1793,  -1449,  -1116,
    -797,   -492,   -201,     74,
     335,    584,    822,   1051,
    1271,   1485,   1695,   1900,
    2104,   2309,   2520,   2740,
    2967,   3202,   3441,   3682,
    3926,   4170,   4414,   4660,
    4909,   5164,   5422,   5684,
    5948,   6213,   6477,   6741,
    7006,   7274,   7545,   7819,
    8096,   8374,   8650,   8919,
    9175,   9417,   9637,   9834,
   10004,  10147,  10264,  10357,
   10429,  10483,  10524,  10555,
   10578,  10595,  10608,  10619,
   10629,  10643,  10662,  10689,
   10726,  10770,  10819,  10871,
   10925,  10981,  11037,  11093,
   11149,  11204,  11258,  11307,
   11350,  11385,  11410,  11423,
   11423,  11410,  11385,  11350,
   11307,  11258,  11204,  11149,
   11093,  11037,  10981,  10925,
   10871,  10819,  10770,  10726,
   10689,  10662,  10643,  10629,
   10619,  10608,  10595,  10578,
   10555,  10524,  10483,  10429,
   10357,  10264,  10147,  10004,
    9834,   9637,   9417,   9175,
    8919,   8650,   8374,   8096,
    7819,   7545,   7274,   7006,
    6741,   6477,   6213,   5948,
    5684,   5422,   5164,   4909,
    4660,   4414,   4170,   3926,
    3682,   3441,   3202,   2967,
    2740,   2520,   2309,   2104,
    1900,   1695,   1485,   1271,
    1051,    822,    584,    335,
      74,   -201,   -492,   -797,
   -1116,  -1449,  -1793,  -2148,
   -2509,  -2875,  -3240,  -3601,
   -3957,  -4306,  -4651,  -4993,
   -5334,  -5675,  -6019,  -6364,
   -6709,  -7053,  -7397,  -7740,
   -8080,  -8420,  -8760,  -9102,
   -9447,  -9796, -10148, -10504,
  -10864, -11228, -11598, -11975,
  -12362, -12764, -13181, -13615,
  -14068, -14541, -15032, -15536,
  -16046, -16558, -17066, -17563,
  -18041, -18494, -18916, -19295,
  -19619, -19879, -20067, -20168,
  -10533, -10837, -11061, -11181,
  -11181, -11061, -10837, -10533,
  -10165,  -9747,  -9292,  -8814,
   -8320,  -7813,  -7301,  -6793,
   -6299,  -5826,  -5378,  -4959,
   -4566,  -4193,  -3838,  -3497,
   -3169,  -2855,  -2556,  -2272,
   -1999,  -1736,  -1481,  -1234,
    -994,   -758,   -528,   -306,
     -93,    109,    299,    473,
     631,    772,    896,   1009,
    1115,   1222,   1335,   1457,
    1587,   1725,   1866,   2008,
    2146,   2274,   2389,   2486,
    2562,   2611,   2629,   2619,
    2582,   2522,   2445,   2357,
    2264,   2171,   2079,   1991,
    1908,   1837,   1778,   1733,
    1700,   1677,   1662,   1654,
    1652,   1656,   1665,   1682,
    1709,   1745,   1787,   1831,
    1876,   1921,   1966,   2012,
    2061,   2116,   2177,   2244,
    2316,   2395,   2477,   2559,
    2637,   2705,   2756,   2786,
    2790,   2767,   2717,   2640,
    2543,   2429,   2302,   2166,
    2028,   1893,   1765,   1648,
    1548,   1465,   1398,   1342,
    1293,   1248,   1202,   1157,
    1113,   1075,   1048,   1034,
    1032,   1038,   1049,   1061,
    1069,   1074,   1076,   1077,
    1077,   1076,   1074,   1069,
    1061,   1049,   1038,   1032,
    1034,   1048,   1075,   1113,
    1157,   1202,   1248,   1293,
    1342,   1398,   1465,   1548,
    1648,   1765,   1893,   2028,
    2166,   2302,   2429,   2543,
    2640,   2717,   2767,   2790,
    2786,   2756,   2705,   2637,
    2559,   2477,   2395,   2316,
    2244,   2177,   2116,   2061,
    2012,   1966,   1921,   1876,
    1831,   1787,   1745,   1709,
    1682,   1665,   1656,   1652,
    1654,   1662,   1677,   1700,
    1733,   1778,   1837,   1908,
    1991,   2079,   2171,   2264,
    2357,   2445,   2522,   2582,
    2619,   2629,   2611,   2562,
    2486,   2389,   2274,   2146,
    2008,   1866,   1725,   1587,
    1457,   1335,   1222,   1115,
    1009,    896,    772,    631,
     473,    299,    109,    -93,
    -306,   -528,   -758,   -994,
   -1234,  -1481,  -1736,  -1999,
   -2272,  -2556,  -2855,  -3169,
   -3497,  -3838,  -4193,  -4566,
   -4959,  -5378,  -5826,  -6299,
   -6793,  -7301,  -7813,  -8320,
   -8814,  -9292,  -9747, -10165,
  -10533, -10837, -11061, -11181,
   -4782,  -5294,  -5738,  -5997,
   -5997,  -5738,  -5294,  -4782,
   -4313,  -3962,  -3749,  -3640,
   -3576,  -3495,  -3370,  -3214,
   -3061,  -2951,  -2900,  -2897,
   -2905,  -2879,  -2790,  -2631,
   -2422,  -2195,  -1980,  -1792,
   -1624,  -1457,  -1272,  -1061,
    -831,   -597,   -379,   -187,
     -25,    110,    220,    301,
     341,    329,    258,    136,
     -12,   -152,   -254,   -295,
    -269,   -185,    -59,     90,
     251,    416,    577,    720,
     823,    866,    827,    702,
     502,    257,     10,   -201,
    -349,   -425,   -434,   -390,
    -310,   -205,    -83,     47,
     180,    304,    411,    492,
     550,    595,    642,    706,
     790,    889,    988,   1068,
    1112,   1116,   1084,   1034,
     984,    956,    963,   1012,
    1103,   1235,   1401,   1593,
    1798,   1996,   2168,   2295,
    2369,   2387,   2357,   2292,
    2202,   2092,   1965,   1820,
    1662,   1509,   1387,   1326,
    1348,   1457,   1637,   1848,
    2039,   2162,   2187,   2115,
    1969,   1793,   1630,   1513,
    1451,   1434,   1438,   1440,
    1424,   1393,   1357,   1334,
    1334,   1357,   1393,   1424,
    1440,   1438,   1434,   1451,
    1513,   1630,   1793,   1969,
    2115,   2187,   2162,   2039,
    1848,   1637,   1457,   1348,
    1326,   1387,   1509,   1662,
    1820,   1965,   2092,   2202,
    2292,   2357,   2387,   2369,
    2295,   2168,   1996,   1798,
    1593,   1401,   1235,   1103,
    1012,    963,    956,    984,
    1034,   1084,   1116,   1112,
    1068,    988,    889,    790,
     706,    642,    595,    550,
     492,    411,    304,    180,
      47,    -83,   -205,   -310,
    -390,   -434,   -425,   -349,
    -201,     10,    257,    502,
     702,    827,    866,    823,
     720,    577,    416,    251,
      90,    -59,   -185,   -269,
    -295,   -254,   -152,    -12,
     136,    258,    329,    341,
     301,    220,    110,    -25,
    -187,   -379,   -597,   -831,
   -1061,  -1272,  -1457,  -1624,
   -1792,  -1980,  -2195,  -2422,
   -2631,  -2790,  -2879,  -2905,
   -2897,  -2900,  -2951,  -3061,
   -3214,  -3370,  -3495,  -3576,
   -3640,  -3749,  -3962,  -4313,
   -4782,  -5294,  -5738,  -5997,
   -6622,  -7134,  -7585,  -7850,
   -7850,  -7585,  -7134,  -6622,
   -6167,  -5844,  -5669,  -5598,
   -5559,  -5486,  -5354,  -5180,
   -5007,  -4880,  -4822,  -4818,
   -4825,  -4790,  -4678,  -4487,
   -4240,  -3979,  -3740,  -3538,
   -3363,  -3189,  -2989,  -2751,
   -2481,  -2201,  -1936,  -1705,
   -1512,  -1355,  -1225,  -1122,
   -1050,  -1019,  -1037,  -1099,
   -1187,  -1271,  -1322,  -1320,
   -1258,  -1141,   -984,   -799,
    -598,   -387,   -174,     25,
     188,    290,    309,    239,
      95,    -93,   -283,   -437,
    -528,   -547,   -502,   -409,
    -284,   -138,     23,    194,
     369,    539,    692,    822,
     930,   1026,   1124,   1239,
    1376,   1531,   1687,   1824,
    1924,   1980,   1999,   1997,
    1998,   2020,   2076,   2172,
    2307,   2476,   2671,   2883,
    3100,   3309,   3494,   3642,
    3749,   3813,   3839,   3831,
    3795,   3735,   3649,   3541,
    3422,   3310,   3232,   3214,
    3276,   3416,   3615,   3833,
    4023,   4145,   4177,   4119,
    3997,   3848,   3708,   3604,
    3546,   3526,   3525,   3526,
    3519,   3500,   3478,   3463,
    3463,   3478,   3500,   3519,
    3526,   3525,   3526,   3546,
    3604,   3708,   3848,   3997,
    4119,   4177,   4145,   4023,
    3833,   3615,   3416,   3276,
    3214,   3232,   3310,   3422,
    3541,   3649,   3735,   3795,
    3831,   3839,   3813,   3749,
    3642,   3494,   3309,   3100,
    2883,   2671,   2476,   2307,
    2172,   2076,   2020,   1998,
    1997,   1999,   1980,   1924,
    1824,   1687,   1531,   1376,
    1239,   1124,   1026,    930,
     822,    692,    539,    369,
     194,     23,   -138,   -284,
    -409,   -502,   -547,   -528,
    -437,   -283,    -93,     95,
     239,    309,    290,    188,
      25,   -174,   -387,   -598,
    -799,   -984,  -1141,  -1258,
   -1320,  -1322,  -1271,  -1187,
   -1099,  -1037,  -1019,  -1050,
   -1122,  -1225,  -1355,  -1512,
   -1705,  -1936,  -2201,  -2481,
   -2751,  -2989,  -3189,  -3363,
   -3538,  -3740,  -3979,  -4240,
   -4487,  -4678,  -4790,  -4825,
   -4818,  -4822,  -4880,  -5007,
   -5180,  -5354,  -5486,  -5559,
   -5598,  -5669,  -5844,  -6167,
   -6622,  -7134,  -7585,  -7850,
  -20254, -20678, -21051, -21273,
  -21273, -21051, -20678, -20254,
  -19872, -19587, -19409, -19303,
  -19209, -19074, -18875, -18629,
  -18372, -18145, -17965, -17826,
  -17691, -17519, -17282, -16977,
  -16623, -16252, -15890, -15550,
  -15222, -14884, -14517, -14113,
  -13680, -13234, -12795, -12378,
  -11984, -11608, -11238, -10872,
  -10512, -10170,  -9854,  -9567,
   -9298,  -9030,  -8740,  -8411,
   -8036,  -7615,  -7158,  -6677,
   -6180,  -5672,  -5160,  -4655,
   -4173,  -3733,  -3349,  -3024,
   -2746,  -2492,  -2235,  -1949,
   -1620,  -1245,   -832,   -393,
      64,    533,   1015,   1510,
    2014,   2518,   3013,   3488,
    3940,   4375,   4805,   5246,
    5703,   6175,   6649,   7109,
    7539,   7932,   8291,   8626,
    8953,   9289,   9646,  10030,
   10441,  10874,  11322,  11776,
   12224,  12658,  13068,  13444,
   13783,  14084,  14353,  14596,
   14815,  15012,  15185,  15334,
   15464,  15587,  15721,  15884,
   16090,  16341,  16625,  16919,
   17191,  17414,  17573,  17665,
   17705,  17715,  17719,  17735,
   17771,  17825,  17889,  17949,
   17998,  18031,  18051,  18061,
   18061,  18051,  18031,  17998,
   17949,  17889,  17825,  17771,
   17735,  17719,  17715,  17705,
   17665,  17573,  17414,  17191,
   16919,  16625,  16341,  16090,
   15884,  15721,  15587,  15464,
   15334,  15185,  15012,  14815,
   14596,  14353,  14084,  13783,
   13444,  13068,  12658,  12224,
   11776,  11322,  10874,  10441,
   10030,   9646,   9289,   8953,
    8626,   8291,   7932,   7539,
    7109,   6649,   6175,   5703,
    5246,   4805,   4375,   3940,
    3488,   3013,   2518,   2014,
    1510,   1015,    533,     64,
    -393,   -832,  -1245,  -1620,
   -1949,  -2235,  -2492,  -2746,
   -3024,  -3349,  -3733,  -4173,
   -4655,  -5160,  -5672,  -6180,
   -6677,  -7158,  -7615,  -8036,
   -8411,  -8740,  -9030,  -9298,
   -9567,  -9854, -10170, -10512,
  -10872, -11238, -11608, -11984,
  -12378, -12795, -13234, -13680,
  -14113, -14517, -14884, -15222,
  -15550, -15890, -16252, -16623,
  -16977, -17282, -17519, -17691,
  -17826, -17965, -18145, -18372,
  -18629, -18875, -19074, -19209,
  -19303, -19409, -19587, -19872,
  -20254, -20678, -21051, -21273,
  -11535, -11757, -11919, -12008,
  -12008, -11919, -11757, -11535,
  -11256, -10920, -10538, -10122,
   -9676,  -9203,  -8712,  -8212,
   -7707,  -7196,  -6684,  -6178,
   -5680,  -5189,  -4707,  -4239,
   -3784,  -3342,  -2912,  -2497,
   -2098,  -1713,  -1341,   -986,
    -647,   -325,    -18,    272,
     540,    786,   1012,   1215,
    1393,   1545,   1670,   1765,
    1828,   1858,   1853,   1813,
    1741,   1640,   1512,   1360,
    1188,   1000,    801,    593,
     380,    163,    -52,   -266,
    -474,   -675,   -867,  -1050,
   -1221,  -1380,  -1523,  -1650,
   -1759,  -1849,  -1921,  -1977,
   -2017,  -2038,  -2040,  -2024,
   -1992,  -1946,  -1885,  -1811,
   -1724,  -1624,  -1510,  -1380,
   -1234,  -1070,   -885,   -676,
    -441,   -180,    105,    412,
     738,   1076,   1423,   1775,
    2128,   2477,   2820,   3151,
    3470,   3772,   4058,   4328,
    4585,   4825,   5050,   5257,
    5449,   5624,   5783,   5925,
    6053,   6171,   6277,   6372,
    6454,   6527,   6592,   6651,
    6704,   6753,   6799,   6842,
    6883,   6921,   6955,   6985,
    7011,   7032,   7047,   7054,
    7054,   7047,   7032,   7011,
    6985,   6955,   6921,   6883,
    6842,   6799,   6753,   6704,
    6651,   6592,   6527,   6454,
    6372,   6277,   6171,   6053,
    5925,   5783,   5624,   5449,
    5257,   5050,   4825,   4585,
    4328,   4058,   3772,   3470,
    3151,   2820,   2477,   2128,
    1775,   1423,   1076,    738,
     412,    105,   -180,   -441,
    -676,   -885,  -1070,  -1234,
   -1380,  -1510,  -1624,  -1724,
   -1811,  -1885,  -1946,  -1992,
   -2024,  -2040,  -2038,  -2017,
   -1977,  -1921,  -1849,  -1759,
   -1650,  -1523,  -1380,  -1221,
   -1050,   -867,   -675,   -474,
    -266,    -52,    163,    380,
     593,    801,   1000,   1188,
    1360,   1512,   1640,   1741,
    1813,   1853,   1858,   1828,
    1765,   1670,   1545,   1393,
    1215,   1012,    786,    540,
     272,    -18,   -325,   -647,
    -986,  -1341,  -1713,  -2098,
   -2497,  -2912,  -3342,  -3784,
   -4239,  -4707,  -5189,  -5680,
   -6178,  -6684,  -7196,  -7707,
   -8212,  -8712,  -9203,  -9676,
  -10122, -10538, -10920, -11256,
  -11535, -11757, -11919, -12008,
   -8542,  -8795,  -8998,  -9117,
   -9117,  -8998,  -8795,  -8542,
   -8246,  -7901,  -7510,  -7091,
   -6663,  -6236,  -5814,  -5389,
   -4951,  -4493,  -4020,  -3544,
   -3063,  -2570,  -2062,  -1550,
   -1055,   -594,   -175,    203,
     543,    843,   1099,   1306,
    1474,   1618,   1759,   1902,
    2044,   2176,   2297,   2411,
    2524,   2627,   2704,   2744,
    2749,   2733,   2705,   2668,
    2619,   2558,   2490,   2431,
    2393,   2373,   2354,   2320,
    2267,   2200,   2119,   2011,
    1866,   1676,   1449,   1198,
     936,    670,    398,    119,
    -159,   -423,   -667,   -897,
   -1128,  -1370,  -1624,  -1883,
   -2145,  -2410,  -2681,  -2954,
   -3216,  -3450,  -3642,  -3786,
   -3886,  -3945,  -3956,  -3909,
   -3803,  -3653,  -3475,  -3278,
   -3060,  -2815,  -2544,  -2252,
   -1944,  -1621,  -1275,   -900,
    -494,    -65,    374,    813,
    1246,   1672,   2083,   2467,
    2811,   3114,   3382,   3626,
    3852,   4060,   4247,   4413,
    4568,   4721,   4875,   5018,
    5137,   5226,   5286,   5325,
    5343,   5338,   5305,   5251,
    5191,   5143,   5116,   5106,
    5106,   5116,   5143,   5191,
    5251,   5305,   5338,   5343,
    5325,   5286,   5226,   5137,
    5018,   4875,   4721,   4568,
    4413,   4247,   4060,   3852,
    3626,   3382,   3114,   2811,
    2467,   2083,   1672,   1246,
     813,    374,    -65,   -494,
    -900,  -1275,  -1621,  -1944,
   -2252,  -2544,  -2815,  -3060,
   -3278,  -3475,  -3653,  -3803,
   -3909,  -3956,  -3945,  -3886,
   -3786,  -3642,  -3450,  -3216,
   -2954,  -2681,  -2410,  -2145,
   -1883,  -1624,  -1370,  -1128,
    -897,   -667,   -423,   -159,
     119,    398,    670,    936,
    1198,   1449,   1676,   1866,
    2011,   2119,   2200,   2267,
    2320,   2354,   2373,   2393,
    2431,   2490,   2558,   2619,
    2668,   2705,   2733,   2749,
    2744,   2704,   2627,   2524,
    2411,   2297,   2176,   2044,
    1902,   1759,   1618,   1474,
    1306,   1099,    843,    543,
     203,   -175,   -594,  -1055,
   -1550,  -2062,  -2570,  -3063,
   -3544,  -4020,  -4493,  -4951,
   -5389,  -5814,  -6236,  -6663,
   -7091,  -7510,  -7901,  -8246,
   -8542,  -8795,  -8998,  -9117,
   -8657,  -8946,  -9175,  -9307,
   -9307,  -9175,  -8946,  -8657,
   -8318,  -7926,  -7489,  -7024,
   -6550,  -6080,  -5617,  -5158,
   -4689,  -4203,  -3707,  -3213,
   -2721,  -2220,  -1708,  -1196,
    -703,   -240,    189,    587,
     957,   1301,   1613,   1889,
    2135,   2369,   2606,   2854,
    3107,   3355,   3595,   3830,
    4062,   4283,   4476,   4626,
    4734,   4812,   4871,   4915,
    4940,   4947,   4943,   4939,
    4946,   4963,   4980,   4984,
    4973,   4951,   4923,   4878,
    4804,   4692,   4552,   4396,
    4235,   4069,   3893,   3703,
    3505,   3306,   3113,   2917,
    2703,   2456,   2170,   1848,
    1497,   1112,    692,    240,
    -225,   -680,  -1109,  -1506,
   -1869,  -2195,  -2478,  -2710,
   -2890,  -3030,  -3143,  -3239,
   -3314,  -3358,  -3370,  -3354,
   -3316,  -3257,  -3171,  -3054,
   -2905,  -2733,  -2549,  -2363,
   -2179,  -1999,  -1827,  -1674,
   -1550,  -1454,  -1373,  -1290,
   -1196,  -1088,   -967,   -835,
    -682,   -500,   -292,    -73,
     134,    320,    484,    633,
     764,    868,    939,    978,
     998,   1014,   1032,   1045,
    1045,   1032,   1014,    998,
     978,    939,    868,    764,
     633,    484,    320,    134,
     -73,   -292,   -500,   -682,
    -835,   -967,  -1088,  -1196,
   -1290,  -1373,  -1454,  -1550,
   -1674,  -1827,  -1999,  -2179,
   -2363,  -2549,  -2733,  -2905,
   -3054,  -3171,  -3257,  -3316,
   -3354,  -3370,  -3358,  -3314,
   -3239,  -3143,  -3030,  -2890,
   -2710,  -2478,  -2195,  -1869,
   -1506,  -1109,   -680,   -225,
     240,    692,   1112,   1497,
    1848,   2170,   2456,   2703,
    2917,   3113,   3306,   3505,
    3703,   3893,   4069,   4235,
    4396,   4552,   4692,   4804,
    4878,   4923,   4951,   4973,
    4984,   4980,   4963,   4946,
    4939,   4943,   4947,   4940,
    4915,   4871,   4812,   4734,
    4626,   4476,   4283,   4062,
    3830,   3595,   3355,   3107,
    2854,   2606,   2369,   2135,
    1889,   1613,   1301,    957,
     587,    189,   -240,   -703,
   -1196,  -1708,  -2220,  -2721,
   -3213,  -3707,  -4203,  -4689,
   -5158,  -5617,  -6080,  -6550,
   -7024,  -7489,  -7926,  -8318,
   -8657,  -8946,  -9175,  -9307,
  -10645, -10976, -11220, -11353,
  -11353, -11220, -10976, -10645,
  -10246,  -9791,  -9302,  -8797,
   -8288,  -7782,  -7284,  -6799,
   -6329,  -5873,  -5432,  -5008,
   -4603,  -4215,  -3843,  -3485,
   -3140,  -2806,  -2478,  -2154,
   -1832,  -1511,  -1189,   -863,
    -527,   -181,    176,    544,
     923,   1312,   1705,   2095,
    2474,   2836,   3173,   3481,
    3759,   4007,   4227,   4422,
    4594,   4748,   4886,   5013,
    5133,   5249,   5367,   5489,
    5617,   5755,   5906,   6074,
    6257,   6459,   6679,   6914,
    7159,   7410,   7664,   7917,
    8166,   8407,   8633,   8837,
    9009,   9135,   9202,   9199,
    9118,   8958,   8720,   8412,
    8047,   7638,   7200,   6745,
    6284,   5822,   5366,   4914,
    4468,   4026,   3589,   3158,
    2733,   2314,   1900,   1490,
    1082,    673,    260,   -158,
    -585,  -1023,  -1473,  -1935,
   -2410,  -2898,  -3399,  -3910,
   -4422,  -4923,  -5399,  -5839,
   -6229,  -6557,  -6812,  -6993,
   -7103,  -7149,  -7141,  -7089,
   -7008,  -6907,  -6795,  -6679,
   -6565,  -6457,  -6360,  -6272,
   -6195,  -6133,  -6089,  -6066,
   -6066,  -6089,  -6133,  -6195,
   -6272,  -6360,  -6457,  -6565,
   -6679,  -6795,  -6907,  -7008,
   -7089,  -7141,  -7149,  -7103,
   -6993,  -6812,  -6557,  -6229,
   -5839,  -5399,  -4923,  -4422,
   -3910,  -3399,  -2898,  -2410,
   -1935,  -1473,  -1023,   -585,
    -158,    260,    673,   1082,
    1490,   1900,   2314,   2733,
    3158,   3589,   4026,   4468,
    4914,   5366,   5822,   6284,
    6745,   7200,   7638,   8047,
    8412,   8720,   8958,   9118,
    9199,   9202,   9135,   9009,
    8837,   8633,   8407,   8166,
    7917,   7664,   7410,   7159,
    6914,   6679,   6459,   6257,
    6074,   5906,   5755,   5617,
    5489,   5367,   5249,   5133,
    5013,   4886,   4748,   4594,
    4422,   4227,   4007,   3759,
    3481,   3173,   2836,   2474,
    2095,   1705,   1312,    923,
     544,    176,   -181,   -527,
    -863,  -1189,  -1511,  -1832,
   -2154,  -2478,  -2806,  -3140,
   -3485,  -3843,  -4215,  -4603,
   -5008,  -5432,  -5873,  -6329,
   -6799,  -7284,  -7782,  -8288,
   -8797,  -9302,  -9791, -10246,
  -10645, -10976, -11220, -11353,
   -9418,  -9776, -10039, -10182,
  -10182, -10039,  -9776,  -9418,
   -8985,  -8499,  -7987,  -7477,
   -6985,  -6524,  -6102,  -5725,
   -5391,  -5094,  -4828,  -4589,
   -4367,  -4156,  -3948,  -3739,
   -3522,  -3291,  -3044,  -2783,
   -2507,  -2216,  -1911,  -1595,
   -1270,   -938,   -603,   -268,
      62,    388,    712,   1033,
    1351,   1666,   1981,   2297,
    2615,   2933,   3246,   3551,
    3845,   4125,   4389,   4633,
    4855,   5057,   5240,   5404,
    5553,   5693,   5827,   5957,
    6084,   6209,   6332,   6450,
    6562,   6667,   6766,   6859,
    6949,   7037,   7124,   7203,
    7271,   7318,   7334,   7309,
    7234,   7106,   6921,   6685,
    6404,   6091,   5756,   5409,
    5058,   4714,   4384,   4069,
    3770,   3487,   3218,   2958,
    2704,   2452,   2200,   1944,
    1680,   1403,   1108,    791,
     451,     84,   -313,   -743,
   -1204,  -1689,  -2192,  -2703,
   -3210,  -3696,  -4147,  -4552,
   -4902,  -5188,  -5405,  -5557,
   -5647,  -5685,  -5684,  -5656,
   -5610,  -5555,  -5496,  -5438,
   -5385,  -5335,  -5287,  -5245,
   -5209,  -5180,  -5156,  -5141,
   -5141,  -5156,  -5180,  -5209,
   -5245,  -5287,  -5335,  -5385,
   -5438,  -5496,  -5555,  -5610,
   -5656,  -5684,  -5685,  -5647,
   -5557,  -5405,  -5188,  -4902,
   -4552,  -4147,  -3696,  -3210,
   -2703,  -2192,  -1689,  -1204,
    -743,   -313,     84,    451,
     791,   1108,   1403,   1680,
    1944,   2200,   2452,   2704,
    2958,   3218,   3487,   3770,
    4069,   4384,   4714,   5058,
    5409,   5756,   6091,   6404,
    6685,   6921,   7106,   7234,
    7309,   7334,   7318,   7271,
    7203,   7124,   7037,   6949,
    6859,   6766,   6667,   6562,
    6450,   6332,   6209,   6084,
    5957,   5827,   5693,   5553,
    5404,   5240,   5057,   4855,
    4633,   4389,   4125,   3845,
    3551,   3246,   2933,   2615,
    2297,   1981,   1666,   1351,
    1033,    712,    388,     62,
    -268,   -603,   -938,  -1270,
   -1595,  -1911,  -2216,  -2507,
   -2783,  -3044,  -3291,  -3522,
   -3739,  -3948,  -4156,  -4367,
   -4589,  -4828,  -5094,  -5391,
   -5725,  -6102,  -6524,  -6985,
   -7477,  -7987,  -8499,  -8985,
   -9418,  -9776, -10039, -10182,
   -9914, -10293, -10579, -10736,
  -10736, -10579, -10293,  -9914,
   -9468,  -8976,  -8464,  -7958,
   -7475,  -7026,  -6624,  -6279,
   -5994,  -5760,  -5564,  -5391,
   -5225,  -5052,  -4865,  -4661,
   -4439,  -4194,  -3927,  -3638,
   -3329,  -3005,  -2679,  -2366,
   -2079,  -1823,  -1603,  -1423,
   -1280,  -1171,  -1086,  -1018,
    -960,   -897,   -817,   -707,
    -559,   -373,   -150,    100,
     365,    638,    914,   1190,
    1462,   1724,   1972,   2199,
    2403,   2587,   2754,   2909,
    3057,   3200,   3340,   3474,
    3603,   3727,   3856,   3994,
    4147,   4315,   4494,   4675,
    4849,   5007,   5145,   5262,
    5353,   5413,   5435,   5417,
    5357,   5259,   5129,   4979,
    4822,   4664,   4510,   4362,
    4218,   4076,   3935,   3796,
    3660,   3521,   3374,   3214,
    3038,   2843,   2628,   2395,
    2150,   1892,   1619,   1330,
    1027,    717,    407,    110,
    -161,   -396,   -592,   -748,
    -862,   -933,   -959,   -940,
    -881,   -789,   -680,   -564,
    -450,   -341,   -240,   -146,
     -55,     34,    119,    193,
     251,    294,    323,    338,
     338,    323,    294,    251,
     193,    119,     34,    -55,
    -146,   -240,   -341,   -450,
    -564,   -680,   -789,   -881,
    -940,   -959,   -933,   -862,
    -748,   -592,   -396,   -161,
     110,    407,    717,   1027,
    1330,   1619,   1892,   2150,
    2395,   2628,   2843,   3038,
    3214,   3374,   3521,   3660,
    3796,   3935,   4076,   4218,
    4362,   4510,   4664,   4822,
    4979,   5129,   5259,   5357,
    5417,   5435,   5413,   5353,
    5262,   5145,   5007,   4849,
    4675,   4494,   4315,   4147,
    3994,   3856,   3727,   3603,
    3474,   3340,   3200,   3057,
    2909,   2754,   2587,   2403,
    2199,   1972,   1724,   1462,
    1190,    914,    638,    365,
     100,   -150,   -373,   -559,
    -707,   -817,   -897,   -960,
   -1018,  -1086,  -1171,  -1280,
   -1423,  -1603,  -1823,  -2079,
   -2366,  -2679,  -3005,  -3329,
   -3638,  -3927,  -4194,  -4439,
   -4661,  -4865,  -5052,  -5225,
   -5391,  -5564,  -5760,  -5994,
   -6279,  -6624,  -7026,  -7475,
   -7958,  -8464,  -8976,  -9468,
   -9914, -10293, -10579, -10736,
   -8191,  -8494,  -8740,  -8883,
   -8883,  -8740,  -8494,  -8191,
   -7858,  -7504,  -7129,  -6729,
   -6293,  -5814,  -5307,  -4795,
   -4295,  -3810,  -3331,  -2850,
   -2358,  -1852,  -1345,   -860,
    -414,    -13,    349,    683,
     996,   1285,   1538,   1739,
    1878,   1950,   1962,   1924,
    1847,   1739,   1598,   1423,
    1218,    993,    763,    543,
     348,    184,     46,    -81,
    -203,   -315,   -405,   -463,
    -482,   -462,   -406,   -328,
    -235,   -128,      6,    179,
     399,    665,    970,   1297,
    1632,   1971,   2322,   2692,
    3079,   3473,   3855,   4203,
    4500,   4740,   4928,   5076,
    5194,   5284,   5340,   5352,
    5307,   5204,   5051,   4864,
    4657,   4434,   4190,   3918,
    3609,   3263,   2885,   2486,
    2077,   1666,   1250,    823,
     385,    -58,   -490,   -895,
   -1260,  -1577,  -1845,  -2068,
   -2254,  -2407,  -2520,  -2582,
   -2592,  -2556,  -2486,  -2394,
   -2290,  -2177,  -2050,  -1896,
   -1708,  -1488,  -1251,  -1008,
    -770,   -542,   -322,   -104,
     117,    340,    551,    736,
     881,    983,   1045,   1074,
    1074,   1045,    983,    881,
     736,    551,    340,    117,
    -104,   -322,   -542,   -770,
   -1008,  -1251,  -1488,  -1708,
   -1896,  -2050,  -2177,  -2290,
   -2394,  -2486,  -2556,  -2592,
   -2582,  -2520,  -2407,  -2254,
   -2068,  -1845,  -1577,  -1260,
    -895,   -490,    -58,    385,
     823,   1250,   1666,   2077,
    2486,   2885,   3263,   3609,
    3918,   4190,   4434,   4657,
    4864,   5051,   5204,   5307,
    5352,   5340,   5284,   5194,
    5076,   4928,   4740,   4500,
    4203,   3855,   3473,   3079,
    2692,   2322,   1971,   1632,
    1297,    970,    665,    399,
     179,      6,   -128,   -235,
    -328,   -406,   -462,   -482,
    -463,   -405,   -315,   -203,
     -81,     46,    184,    348,
     543,    763,    993,   1218,
    1423,   1598,   1739,   1847,
    1924,   1962,   1950,   1878,
    1739,   1538,   1285,    996,
     683,    349,    -13,   -414,
    -860,  -1345,  -1852,  -2358,
   -2850,  -3331,  -3810,  -4295,
   -4795,  -5307,  -5814,  -6293,
   -6729,  -7129,  -7504,  -7858,
   -8191,  -8494,  -8740,  -8883,
   -4178,  -4571,  -4921,  -5135,
   -5135,  -4921,  -4571,  -4178,
   -3785,  -3394,  -3002,  -2642,
   -2366,  -2211,  -2161,  -2160,
   -2147,  -2088,  -1980,  -1821,
   -1590,  -1255,   -810,   -298,
     207,    641,    974,   1214,
    1371,   1438,   1396,   1249,
    1041,    841,    705,    652,
     674,    758,    898,   1091,
    1318,   1532,   1677,   1713,
    1639,   1480,   1263,    999,
     698,    391,    130,    -30,
     -61,     28,    199,    412,
     642,    873,   1083,   1234,
    1290,   1242,   1114,    949,
     783,    638,    531,    485,
     532,    690,    947,   1251,
    1540,   1767,   1912,   1974,
    1946,   1816,   1573,   1237,
     856,    493,    195,    -21,
    -158,   -218,   -197,   -101,
      40,    168,    227,    190,
      62,   -135,   -384,   -676,
    -997,  -1314,  -1574,  -1727,
   -1750,  -1654,  -1472,  -1238,
    -975,   -706,   -462,   -282,
    -200,   -223,   -324,   -461,
    -594,   -705,   -775,   -779,
    -681,   -460,   -133,    253,
     639,    982,   1265,   1483,
    1625,   1669,   1604,   1447,
    1248,   1063,    931,    865,
     865,    931,   1063,   1248,
    1447,   1604,   1669,   1625,
    1483,   1265,    982,    639,
     253,   -133,   -460,   -681,
    -779,   -775,   -705,   -594,
    -461,   -324,   -223,   -200,
    -282,   -462,   -706,   -975,
   -1238,  -1472,  -1654,  -1750,
   -1727,  -1574,  -1314,   -997,
    -676,   -384,   -135,     62,
     190,    227,    168,     40,
    -101,   -197,   -218,   -158,
     -21,    195,    493,    856,
    1237,   1573,   1816,   1946,
    1974,   1912,   1767,   1540,
    1251,    947,    690,    532,
     485,    531,    638,    783,
     949,   1114,   1242,   1290,
    1234,   1083,    873,    642,
     412,    199,     28,    -61,
     -30,    130,    391,    698,
     999,   1263,   1480,   1639,
    1713,   1677,   1532,   1318,
    1091,    898,    758,    674,
     652,    705,    841,   1041,
    1249,   1396,   1438,   1371,
    1214,    974,    641,    207,
    -298,   -810,  -1255,  -1590,
   -1821,  -1980,  -2088,  -2147,
   -2160,  -2161,  -2211,  -2366,
   -2642,  -3002,  -3394,  -3785,
   -4178,  -4571,  -4921,  -5135,
   -4733,  -5126,  -5504,  -5744,
   -5744,  -5504,  -5126,  -4733,
   -4391,  -4072,  -3704,  -3247,
   -2735,  -2261,  -1912,  -1700,
   -1556,  -1380,  -1116,   -781,
    -443,   -155,     86,    329,
     620,    962,   1297,   1547,
    1667,   1664,   1584,   1467,
    1322,   1126,    855,    517,
     158,   -164,   -412,   -592,
    -733,   -864,   -990,  -1091,
   -1149,  -1166,  -1172,  -1206,
   -1287,  -1401,  -1507,  -1568,
   -1571,  -1530,  -1463,  -1374,
   -1242,  -1036,   -745,   -385,
      -4,    351,    657,    922,
    1167,   1403,   1615,   1771,
    1853,   1870,   1860,   1867,
    1913,   1990,   2068,   2124,
    2156,   2178,   2204,   2229,
    2231,   2181,   2065,   1890,
    1681,   1462,   1249,   1044,
     849,    666,    505,    377,
     284,    224,    188,    168,
     154,    139,    118,     88,
      48,      1,    -45,    -82,
    -105,   -113,   -108,    -92,
     -63,    -19,     42,    118,
     201,    282,    349,    399,
     434,    459,    481,    503,
     522,    536,    543,    550,
     565,    594,    636,    681,
     717,    736,    741,    739,
     739,    741,    736,    717,
     681,    636,    594,    565,
     550,    543,    536,    522,
     503,    481,    459,    434,
     399,    349,    282,    201,
     118,     42,    -19,    -63,
     -92,   -108,   -113,   -105,
     -82,    -45,      1,     48,
      88,    118,    139,    154,
     168,    188,    224,    284,
     377,    505,    666,    849,
    1044,   1249,   1462,   1681,
    1890,   2065,   2181,   2231,
    2229,   2204,   2178,   2156,
    2124,   2068,   1990,   1913,
    1867,   1860,   1870,   1853,
    1771,   1615,   1403,   1167,
     922,    657,    351,     -4,
    -385,   -745,  -1036,  -1242,
   -1374,  -1463,  -1530,  -1571,
   -1568,  -1507,  -1401,  -1287,
   -1206,  -1172,  -1166,  -1149,
   -1091,   -990,   -864,   -733,
    -592,   -412,   -164,    158,
     517,    855,   1126,   1322,
    1467,   1584,   1664,   1667,
    1547,   1297,    962,    620,
     329,     86,   -155,   -443,
    -781,  -1116,  -1380,  -1556,
   -1700,  -1912,  -2261,  -2735,
   -3247,  -3704,  -4072,  -4391,
   -4733,  -5126,  -5504,  -5744,
   -6693,  -7200,  -7630,  -7883,
   -7883,  -7630,  -7200,  -6693,
   -6181,  -5688,  -5211,  -4745,
   -4306,  -3923,  -3624,  -3409,
   -3242,  -3081,  -2899,  -2692,
   -2463,  -2208,  -1910,  -1555,
   -1144,   -710,   -303,     37,
     290,    461,    555,    573,
     506,    351,    120,   -156,
    -439,   -702,   -935,  -1136,
   -1304,  -1432,  -1516,  -1559,
   -1578,  -1603,  -1659,  -1755,
   -1883,  -2030,  -2189,  -2360,
   -2541,  -2722,  -2879,  -2981,
   -3002,  -2926,  -2761,  -2530,
   -2258,  -1962,  -1651,  -1328,
    -995,   -665,   -347,    -51,
     225,    487,    743,   1001,
    1263,   1529,   1796,   2061,
    2328,   2597,   2864,   3119,
    3344,   3520,   3633,   3677,
    3653,   3566,   3425,   3239,
    3021,   2781,   2526,   2265,
    2010,   1772,   1563,   1387,
    1242,   1119,   1007,    899,
     803,    730,    686,    670,
     669,    669,    663,    659,
     673,    722,    811,    939,
    1100,   1287,   1496,   1732,
    1996,   2285,   2585,   2882,
    3165,   3427,   3663,   3868,
    4035,   4158,   4236,   4275,
    4286,   4281,   4270,   4262,
    4262,   4270,   4281,   4286,
    4275,   4236,   4158,   4035,
    3868,   3663,   3427,   3165,
    2882,   2585,   2285,   1996,
    1732,   1496,   1287,   1100,
     939,    811,    722,    673,
     659,    663,    669,    669,
     670,    686,    730,    803,
     899,   1007,   1119,   1242,
    1387,   1563,   1772,   2010,
    2265,   2526,   2781,   3021,
    3239,   3425,   3566,   3653,
    3677,   3633,   3520,   3344,
    3119,   2864,   2597,   2328,
    2061,   1796,   1529,   1263,
    1001,    743,    487,    225,
     -51,   -347,   -665,   -995,
   -1328,  -1651,  -1962,  -2258,
   -2530,  -2761,  -2926,  -3002,
   -2981,  -2879,  -2722,  -2541,
   -2360,  -2189,  -2030,  -1883,
   -1755,  -1659,  -1603,  -1578,
   -1559,  -1516,  -1432,  -1304,
   -1136,   -935,   -702,   -439,
    -156,    120,    351,    506,
     573,    555,    461,    290,
      37,   -303,   -710,  -1144,
   -1555,  -1910,  -2208,  -2463,
   -2692,  -2899,  -3081,  -3242,
   -3409,  -3624,  -3923,  -4306,
   -4745,  -5211,  -5688,  -6181,
   -6693,  -7200,  -7630,  -7883,
   -8495,  -8899,  -9239,  -9439,
   -9439,  -9239,  -8899,  -8495,
   -8073,  -7636,  -7170,  -6670,
   -6158,  -5680,  -5281,  -4972,
   -4723,  -4484,  -4218,  -3921,
   -3609,  -3300,  -2996,  -2685,
   -2358,  -2023,  -1709,  -1455,
   -1285,  -1204,  -1202,  -1267,
   -1398,  -1597,  -1858,  -2159,
   -2466,  -2745,  -2980,  -3168,
   -3319,  -3437,  -3518,  -3555,
   -3548,  -3510,  -3469,  -3450,
   -3457,  -3477,  -3487,  -3470,
   -3422,  -3347,  -3248,  -3119,
   -2941,  -2690,  -2360,  -1964,
   -1532,  -1095,   -669,   -257,
     147,    542,    912,   1234,
    1496,   1706,   1889,   2071,
    2263,   2459,   2642,   2802,
    2940,   3067,   3192,   3309,
    3394,   3422,   3387,   3300,
    3190,   3079,   2973,   2864,
    2742,   2611,   2493,   2413,
    2385,   2399,   2432,   2463,
    2490,   2524,   2581,   2663,
    2754,   2831,   2882,   2915,
    2949,   3009,   3100,   3211,
    3324,   3429,   3532,   3648,
    3789,   3947,   4097,   4216,
    4298,   4352,   4400,   4456,
    4520,   4578,   4619,   4645,
    4671,   4717,   4787,   4866,
    4930,   4966,   4976,   4975,
    4975,   4976,   4966,   4930,
    4866,   4787,   4717,   4671,
    4645,   4619,   4578,   4520,
    4456,   4400,   4352,   4298,
    4216,   4097,   3947,   3789,
    3648,   3532,   3429,   3324,
    3211,   3100,   3009,   2949,
    2915,   2882,   2831,   2754,
    2663,   2581,   2524,   2490,
    2463,   2432,   2399,   2385,
    2413,   2493,   2611,   2742,
    2864,   2973,   3079,   3190,
    3300,   3387,   3422,   3394,
    3309,   3192,   3067,   2940,
    2802,   2642,   2459,   2263,
    2071,   1889,   1706,   1496,
    1234,    912,    542,    147,
    -257,   -669,  -1095,  -1532,
   -1964,  -2360,  -2690,  -2941,
   -3119,  -3248,  -3347,  -3422,
   -3470,  -3487,  -3477,  -3457,
   -3450,  -3469,  -3510,  -3548,
   -3555,  -3518,  -3437,  -3319,
   -3168,  -2980,  -2745,  -2466,
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   11692,  11617,  11474,  11267,
   10998,  10671,  10294,   9876,
    9425,   8946,   8447,   7940,
    7428,   6916,   6410,   5916,
    5438,   4978,   4536,   4114,
    3711,   3326,   2960,   2612,
    2277,   1952,   1636,   1329,
    1029,    732,    437,    146,
    -143,   -434,   -730,  -1027,
   -1327,  -1633,  -1950,  -2275,
   -2610,  -2958,  -3324,  -3709,
   -4112,  -4534,  -4976,  -5437,
   -5915,  -6409,  -6916,  -7428,
   -7939,  -8447,  -8946,  -9426,
   -9878, -10295, -10674, -11001,
  -11270, -11478, -11626, -11705,
  -11575, -11722, -11833, -11894,
  -11894, -11833, -11722, -11575,
  -11396, -11186, -10947, -10684,
  -10398, -10090,  -9760,  -9410,
   -9046,  -8667,  -8275,  -7870,
   -7452,  -7023,  -6584,  -6134,
   -5677,  -5211,  -4737,  -4257,
   -3771,  -3280,  -2784,  -2284,
   -1782,  -1276,   -767,   -256,
     256,    767,   1276,   1782,
    2284,   2784,   3280,   3771,
    4257,   4737,   5211,   5677,
    6134,   6584,   7023,   7452,
    7870,   8275,   8667,   9046,
    9410,   9760,  10090,  10398,
   10684,  10947,  11186,  11396,
   11575,  11722,  11833,  11894,
   11894,  11833,  11722,  11575,
   11396,  11186,  10947,  10684,
   10398,  10090,   9760,   9410,
    9046,   8667,   8275,   7870,
    7452,   7023,   6584,   6134,
    5677,   5211,   4737,   4257,
    3771,   3280,   2784,   2284,
    1782,   1276,    767,    256,
    -256,   -767,  -1276,  -1782,
   -2284,  -2784,  -3280,  -3771,
   -4257,  -4737,  -5211,  -5677,
   -6134,  -6584,  -7023,  -7452,
   -7870,  -8275,  -8667,  -9046,
   -9410,  -9760, -10090, -10398,
  -10684, -10947, -11186, -11396,
  -11575, -11722, -11833, -11894,
  -11894, -11833, -11722, -11575,
  -11396, -11186, -10947, -10684,
  -10398, -10090,  -9760,  -9410,
   -9046,  -8667,  -8275,  -7870,
   -7452,  -7023,  -6584,  -6134,
   -5677,  -5211,  -4737,  -4257,
   -3771,  -3280,  -2784,  -2284,
   -1782,  -1276,   -767,   -256,
     256,    767,   1276,   1782,
    2284,   2784,   3280,   3771,
    4257,   4737,   5211,   5677,
    6134,   6584,   7023,   7452,
    7870,   8275,   8667,   9046,
    9410,   9760,  10090,  10398,
   10684,  10947,  11186,  11396,
   11575,  11722,  11833,  11894,
   11894,  11833,  11722,  11575,
   11396,  11186,  10947,  10684,
   10398,  10090,   9760,   9410,
    9046,   8667,   8275,   7870,
    7452,   7023,   6584,   6134,
    5677,   5211,   4737,   4257,
    3771,   3280,   2784,   2284,
    1782,   1276,    767,    256,
    -256,   -767,  -1276,  -1782,
   -2284,  -2784,  -3280,  -3771,
   -4257,  -4737,  -5211,  -5677,
   -6134,  -6584,  -7023,  -7452,
   -7870,  -8275,  -8667,  -9046,
   -9410,  -9760, -10090, -10398,
  -10684, -10947, -11186, -11396,
  -11575, -11722, -11833, -11894,
};


const int16_t* wavetables_table[] = {
  wav_integrated_waves,
};


}  // namespace plaits
